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A and B are events of an experiment such that 0<P(A), P(B)<1. If P\left(B^{\prime}\right)>P\left(A^{\prime}\right), then

Option: 1

P\left(A \cap B^{\prime}\right)<P\left(A^{\prime} \cap B\right)


Option: 2

P\left(A \cap B^{\prime}\right)=P\left(A^{\prime} \cap B\right)


Option: 3

P(B / A)<P(A / B)


Option: 4

P(B / A)>P(A / B)


Answers (1)

best_answer

\text{Given}\: \: P\left(B^{\prime}\right)>P\left(A^{\prime}\right)

\begin{aligned} & \Rightarrow P(B)<P(A) \\ \\& \Rightarrow \quad P(A)=P\left(A \cap B^{\prime}\right)+P(A \cap B) \end{aligned}

                                   \begin{aligned} & >P(B) \\ \\& =P\left(A^{\prime} \cap B\right)+P(A \cap B) \end{aligned}

\\\Rightarrow P\left(A \cap B^{\prime}\right)>P\left(A^{\prime} \cap B\right)\\ \\\Rightarrow(A) \: \text{is false and so is} \: (B)

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sudhir.kumar

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