Discrete Probability Distributions/Binomial Distributions Question 15 Answer Guessing

imgres.jpg

You are taking a multiple choice quiz that consists of five questions.  Each question has four possible answers, only one which is correct.  To complete the quiz, you randomly guess the answer to each questions.  To three significant digits, find the probability of guessing:

  1. exactly three questions correctly.
    {#1}

  2. at least three answers correctly.
    {#2}

  3. less than three answers correctly.
    {#3}
]]> 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 3.0000000 0.3333333 0 <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><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>25</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sola</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mi>a</mi></apply><mo>*</mo><msup><mi>p</mi><mi>a</mi></msup><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>p</mi></mrow></mfenced><mrow><mi>n</mi><mo>-</mo><mi>a</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solb</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mi>b</mi></apply><mo>*</mo><msup><mi>p</mi><mi>b</mi></msup><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>p</mi></mrow></mfenced><mrow><mi>n</mi><mo>-</mo><mi>b</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solc</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mi>c</mi></apply><mo>*</mo><msup><mi>p</mi><mi>c</mi></msup><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>p</mi></mrow></mfenced><mrow><mi>n</mi><mo>-</mo><mi>c</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sold</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mi>d</mi></apply><mo>*</mo><msup><mi>p</mi><mi>d</mi></msup><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>p</mi></mrow></mfenced><mrow><mi>n</mi><mo>-</mo><mi>d</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sole</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mi>e</mi></apply><mo>*</mo><msup><mi>p</mi><mi>e</mi></msup><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>p</mi></mrow></mfenced><mrow><mi>n</mi><mo>-</mo><mi>e</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solf</mi><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">C</csymbol><mi>n</mi><mi>f</mi></apply><mo>*</mo><msup><mi>p</mi><mi>f</mi></msup><mo>*</mo><msup><mfenced><mrow><mn>1</mn><mo>-</mo><mi>p</mi></mrow></mfenced><mrow><mi>n</mi><mo>-</mo><mi>f</mi></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solg</mi><mo>=</mo><mi>sold</mi><mo>+</mo><mi>sole</mi><mo>+</mo><mi>solf</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solh</mi><mo>=</mo><mi>sola</mi><mo>+</mo><mi>solb</mi><mo>+</mo><mi>solc</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sold</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.087891</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solg</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.10352</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>solh</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.89648</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]>