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  • How to solve this problem- Two integers are selected at random from the set {1,2,...........11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is:

 

Two integers are selected at random from the set {1,2,...........11}. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is:

  • Option 1)

     

    \frac{3}{5}

  • Option 2)

     

    \frac{1}{2}

  • Option 3)

     

    \frac{7}{10}

  • Option 4)

     

    \frac{2}{5}

Answers (1)

best_answer

 

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.

 

from 1 to 11 , 6 = odd 5= even 

P\left ( \frac{number\; are\; even}{sum\; are\; even} \right )=\frac{^{5}\textrm{C}_{2}}{^{5}\textrm{C}_{2}+^{6}\textrm{C}_{2}}=\frac{10}{10+15}=\frac{2}{5}


Option 1)

 

\frac{3}{5}

Option 2)

 

\frac{1}{2}

Option 3)

 

\frac{7}{10}

Option 4)

 

\frac{2}{5}
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