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If A and B are two events such that P(A)=0.3, P(B)=0.25 , P(A \cap B)=0.2, then P\left(\left(\frac{A^C}{B^C}\right)^C\right) is equal to 

Option: 1

\frac{2}{15}

 

 

 


Option: 2

\frac{11}{15}
 


Option: 3

\frac{13}{15}


Option: 4

\frac{14}{15}


Answers (1)

best_answer

\begin{aligned} P\left(\left(\frac{A^C}{B^C}\right)^C\right) & =1-P\left(\frac{A^C}{B^C}\right) \\ \\& =1-\frac{P\left(A^C \cap B^C\right)}{P\left(B^C\right)} \\ \\& =1-\frac{1-P(A \cup B)}{1-P(B)} \end{aligned}

                                 \begin{aligned} & =1-\frac{1-P(A)-P(B)+P(A \cap B)}{1-P(B)} \\ \\& =1-\frac{0.65}{0.75}=1-\frac{13}{15}=\frac{2}{15} \end{aligned}

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