If P\left ( A\cap B \right ) = \frac{7}{10} \: and\: P \left ( B \right )= \frac{17}{20}   its P\left ( \frac{A}{B} \right ) equals

  • Option 1)

    \frac{14}{17}

  • Option 2)

    \frac{17}{20}

  • Option 3)

    \frac{7}{8}

  • Option 4)

    \frac{1}{8}

 

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{7}{10}}{\frac{17}{20}}=\frac{\frac{7}{10}}{\frac{17}{20}} =\frac{7\times 20}{17\times 10} =\frac{14}{17}


Option 1)

\frac{14}{17}

Correct

Option 2)

\frac{17}{20}

Incorrect

Option 3)

\frac{7}{8}

Incorrect

Option 4)

\frac{1}{8}

Incorrect

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