Let P\left ( A \right )=\frac{7}{13}\: P\left ( B \right )=\frac{9}{13}\:a,d, p \left ( A\cap B \right )=\frac{4}{3}  then P\left ( \frac{A^{'}}{B} \right ) is equate

  • Option 1)

    \frac{6}{13}

  • Option 2)

    \frac{4}{13}

  • Option 3)

    \frac{4}{9}

  • Option 4)

    \frac{5}{9}

 

Answers (1)

 

Conditional Probability -

 

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

and

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

 

- wherein

where P\left ( \frac{A}{B} \right ) probability of A when B already happened.

 

 P(\frac{A}{B})=\frac{P(A\cap B)}{P(B)} =\frac{\frac{4}{13}}{\frac{9}{13}} =\frac{4}{13}\times \frac{13}{9} =\frac{4}{9}

P(\frac{A'}{B})=1-\frac{4}{9} =\frac{5}{9}


Option 1)

\frac{6}{13}

Incorrect

Option 2)

\frac{4}{13}

Incorrect

Option 3)

\frac{4}{9}

Incorrect

Option 4)

\frac{5}{9}

Correct

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