Question 1

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Question text

Dos successos A i B tenen la mateixa probabilitat P left parenthesis A right parenthesis equals P left parenthesis B right parenthesis equals 1 half. La probabilitat de que ocorrega uno dels successos sabent que ha ocorregut l'altre és igual a 0.3 Quina és la probabilitat de que no ocorrega cap dels successos?

Sabem:

P left parenthesis A right parenthesis equals P left parenthesis B right parenthesis equals 0.5 P left parenthesis A divided by B right parenthesis equals P left parenthesis B divided by A right parenthesis equals

Sabem: P left parenthesis A with bar on top intersection B with bar on top right parenthesis equals P left parenthesis stack A union B with bar on top right parenthesis equals 1 minus P left parenthesis A union B right parenthesis equals 1 minus left square bracket P left parenthesis A right parenthesis plus P left parenthesis B right parenthesis minus P left parenthesis A intersection B right parenthesis right square bracket

Com P left parenthesis A divided by B right parenthesis equals fraction numerator P left parenthesis A intersection B right parenthesis over denominator P left parenthesis B right parenthesis end fraction, tenim que P left parenthesis A intersection B right parenthesis equals P left parenthesis A divided by B right parenthesis times P left parenthesis B right parenthesis equals

Per tant P left parenthesis A with bar on top intersection B with bar on top right parenthesis equals

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