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14.Probability
hard
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
A
$\frac {7}{10}$
B
$\frac {1}{2}$
C
$\frac {2}{5}$
D
$\frac {3}{5}$
(JEE MAIN-2019)
Solution
$\mathrm{P}=\frac{\text { both number is even }}{\text { number of ways selecting two numbers such that their sum is even. }}$
$ = \frac{{{\,^5}{C_2}}}{{^5{C_2} + {\,^6}{C_2}}} = \frac{{10}}{{10 + 15}} = \frac{{10}}{{25}} = \frac{2}{5}$
Standard 11
Mathematics
