Pre-Calc/Chapter 9: Discrete Mathematics/9.1 Basic Combinatorics/9.1.1 Solve Apps: Multiplication Principle Auto Accessories A person ordering a certain model of car can choose any of #c colors, either manual or automatic transmission, and any of #a audio systems. How many ways are there to order this model of car?

]]> 1.0000000 0.3333333 0 0 #answer]]> Great job!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mi>c</mi><mo>*</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> License Plates How many automobile license plates can be made involving #a letters followed by #b digits? (Repetition is allowed)

]]> 1.0000000 0.3333333 0 0 #answer]]> Nice job!

]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><msup><mn>26</mn><mi>a</mi></msup><mo>*</mo><msup><mn>10</mn><mi>b</mi></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<session lang="en" version="2.0"><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></data></localData></question> How many letters/numbers available for each spot?

]]> t

]]> Pre-Calc/Chapter 9: Discrete Mathematics/9.1 Basic Combinatorics/9.1.2 Evaluate Factorial, Combination, or Permulations Evaluating Combinations Evaluate «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«maction actiontype=¨argument¨»«mrow/»«/maction»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msub»«msub»«mi»C«/mi»«mrow»«mo»#«/mo»«mi»r«/mi»«/mrow»«/msub»«/math»

]]> 1.0000000 0.3333333 0 0 #answer]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>13</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mi>r</mi></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Evaluating Factorials Evaluate #n!

]]> 1.0000000 0.3333333 0 0 #answer]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>11</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mi>n</mi><mo>!</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Evaluating Permutations Evaluate «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub»«maction actiontype=¨argument¨»«mrow/»«/maction»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msub»«msub»«mi»P«/mi»«mrow»«mo»#«/mo»«mi»r«/mi»«/mrow»«/msub»«/math»

]]> 1.0000000 0.3333333 0 0 #answer]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>13</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">V</csymbol><mi>n</mi><mi>r</mi></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Pre-Calc/Chapter 9: Discrete Mathematics/9.1 Basic Combinatorics/9.1.3 Decide between Permutations and Combinations Permutations vs. Combinations #c cards are selected from a deck of 52 to form a hand for a certain card game. This example describes a permutation.

]]> 1.0000000 1.0000000 0 True Great job. The order in which the cards are drawn doesn't matter.

]]> False Does the order in which are card are drawn matter?

]]> 1.0000000 0.3333333 0 0 #answer]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>3</mn><mo>.</mo><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mi>m</mi><mo>*</mo><mo>(</mo><mi>m</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>m</mi><mo>-</mo><mn>2</mn><mo>)</mo><mo>*</mo><mi>w</mi><mo>*</mo><mo>(</mo><mi>w</mi><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Pre-Calc/Chapter 9: Discrete Mathematics/9.1 Basic Combinatorics/9.1.5 Solve Apps: Permutations Baseball Lineups Coach Zweigle has #p baseball players. How many 9-player starting lineups can he create?

]]> 1.0000000 0.3333333 0 0 #answer]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>10</mn><mo>.</mo><mo>.</mo><mn>14</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">V</csymbol><mi>p</mi><mn>9</mn></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"><![CDATA[<session lang="en" version="2.0"><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">PR</csymbol><mn>9</mn><mi>p</mi></apply></math></input></command></group></session>]]></data></localData></question> Pre-Calc/Chapter 9: Discrete Mathematics/9.2 The Binomial Theorem/9.2.1 Expand Binomial Expression Expand the Binomial «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mn»3«/mn»«mi»x«/mi»«mo»+«/mo»«mn»5«/mn»«msup»«mo»)«/mo»«mn»3«/mn»«/msup»«mo»=«/mo»«/math»

]]> 1.0000000 0.3333333 0 true true abc «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»9«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»30«/mn»«mi»x«/mi»«mo»+«/mo»«mn»25«/mn»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»27«/mn»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»+«/mo»«mn»135«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»225«/mn»«mi»x«/mi»«mo»+«/mo»«mn»125«/mn»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»27«/mn»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»+«/mo»«mn»135«/mn»«msup»«mi»x«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«mn»135«/mn»«mi»x«/mi»«mo»+«/mo»«mn»125«/mn»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»9«/mn»«msup»«mi»x«/mi»«mn»6«/mn»«/msup»«mo»+«/mo»«mn»15«/mn»«msup»«mi»x«/mi»«mn»3«/mn»«/msup»«mo»+«/mo»«mn»15625«/mn»«/math»

]]> <question><correctAnswers><correctAnswer></correctAnswer></correctAnswers></question> Pre-Calc/Chapter 9: Discrete Mathematics/9.2 The Binomial Theorem/9.2.2 Evaluate a Binomial Coefficient Evaluating Combinations Evaluate combinations of #n objects chosen #r at a time.

]]> 1.0000000 0.3333333 0 0 #answer]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>8</mn><mo>.</mo><mo>.</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mi>r</mi></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Pre-Calc/Chapter 9: Discrete Mathematics/9.2 The Binomial Theorem/9.2.3 Find Coefficient of Given Term in Expansion Find coefficient of a given term Find the coefficient of the «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup»«mi»x«/mi»«mrow»«mo»#«/mo»«mi»a«/mi»«/mrow»«/msup»«msup»«mi»y«/mi»«mrow»«mo»#«/mo»«mi»b«/mi»«/mrow»«/msup»«/math» term in the expansion of «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»(«/mo»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«msup»«mo»)«/mo»«mrow»«mo»#«/mo»«mi»n«/mi»«/mrow»«/msup»«/math»

]]> 1.0000000 0.3333333 0 0 #answer]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>6</mn><mo>.</mo><mo>.</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>n</mi><mo>-</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mi>a</mi></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="cas">add</data><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Pre-Calc/Chapter 9: Discrete Mathematics/9.3 Probability/9.3.1 Calculate Probability (Dice) Probability of sum of two dice Two 6-sided dice are rolled. What is the probability the sum of the two numbers will be 5?

]]> 1.0000000 0.3333333 0 0 19]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>9</mn></mfrac></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Pre-Calc/Chapter 9: Discrete Mathematics/9.3 Probability/9.3.4 Calculate Probability of Card Hand Probability of Card Hand (one condition) A 5-card hand is dealt from a deck of 52 cards. What is the probability that #n are queens? (Use the CAS tool to solve, then enter answer as fraction)

]]> 1.0000000 0.3333333 0 0 #answer]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>0</mn><mo>.</mo><mo>.</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mfrac><mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mn>4</mn><mi>n</mi></apply><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mn>48</mn><mrow><mn>5</mn><mo>-</mo><mi>n</mi></mrow></apply></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mn>52</mn><mn>5</mn></apply></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="cas">add</data><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Probability of Card Hand (two conditions) A 5-card hand is dealt from a deck of 52 cards. What is the probability that #n are kings, and the other cards aces? (Use the CAS tool to solve, then enter answer as fraction)

]]> 1.0000000 0.3333333 0 0 #answer]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><mfrac><mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mn>4</mn><mi>n</mi></apply><mo>*</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mn>4</mn><mrow><mn>5</mn><mo>-</mo><mi>n</mi></mrow></apply></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mn>52</mn><mn>5</mn></apply></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>n</mi><mi>s</mi><mi>w</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="cas">add</data><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Pre-Calc/Chapter 9: Discrete Mathematics/9.3 Probability/9.3.5 Solve Apps: Probability Probability: Multiple Slips of Paper A box contains 4 slips of paper, on each of which is written the number 1, 2, 3, or 4. A slip of paper is drawn and the number on it is noted. That slip is put aside, another drawn, and the number on it noted. What is the probability that:

A) the sum of the two numbers is 5?

B) the first number drawn is a 2 and the second number is NOT a 5?

C) the sum of the numbers is NOT 10?

]]> 1.0000000 0.3333333 0 0 13141]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac><mspace linebreak="newline"/><mfrac><mn>1</mn><mn>4</mn></mfrac><mspace linebreak="newline"/><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">33% 33% 34%</data><data name="inputField">popupEditor</data><data name="casSession">null</data></localData></question> Pre-Calc/Chapter 9: Discrete Mathematics/Binomial Probability Boys and Girls In South Africa, the probability of a child being born female is 51.2%. What is the probability of a family of five children having exactly 4 girls? (Round to hundredths)

]]> 1.0000000 0.3333333 0 0 0.17]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>17</mn></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Boys and Girls (2) In South Africa, the probability of a child being born female is 51.2%. What is the probability of a family of five children having at least 4 girls? (Round to thousandths)

]]> 1.0000000 0.3333333 0 0 .203]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>.</mo><mn>203</mn></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Defective Batteries Duracell knows that a battery coming off the assembly line has a probability of .035 of being defective. If four units are selected at random during the course of a workday, what is the probability that none of the four batteries are defective? (Round to hundredths)

]]> 1.0000000 0.3333333 0 0 .87]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>.</mo><mn>87</mn></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Free Throws Logan is a 19% free throw shooter. If he shoots 10 free throws in a row, what is the probability he makes exactly 6 of them? (Round to thousandths)

]]> 1.0000000 0.3333333 0 0 .004]]> <question><wirisCasSession><![CDATA[<session lang="en" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="en">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>random</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>answer</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mn>10</mn><mi>n</mi></apply><mo>*</mo><mo>(</mo><mo>.</mo><mn>19</mn><msup><mo>)</mo><mi>n</mi></msup><mo>*</mo><mo>(</mo><mo>.</mo><mn>81</mn><msup><mo>)</mo><mrow><mn>10</mn><mo>-</mo><mi>n</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>.</mo><mn>004</mn></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Medical Treatment A new medical treatment procedure boasts a 93% success rate for any given patient. If twelve patients at a hospital undergo this treatment, what is the probability that at least 10 of the twelve recover from their illness? (round to thousandths)

]]> 1.0000000 0.3333333 0 0 .953]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>.</mo><mn>953</mn></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question> Renting Cars Enterprise has 30 cars available for rental--22 mid-size cars, and 8 compact cars. If two cars are selected at random, what is the probability that both are mid-size cars? (Round to hundredths)

]]> 1.0000000 0.3333333 0 0 0.53]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.53</mn></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession">null</data></localData></question>