JEE PYQ: Probability Question 45
Question 45 - 2019 (11 Jan Shift 1)
Two integers are selected at random from the set ${1, 2, \ldots, 11}$. Given that the sum of selected numbers is even, the conditional probability that both the numbers are even is:
(1) $\frac{7}{10}$
(2) $\frac{1}{2}$
(3) $\frac{2}{5}$
(4) $\frac{3}{5}$
Show Answer
Answer: (3)
Solution
Even sum: both even or both odd. $P(E_1) = {}^5C_2 = 10$ (both even). $P(E_2) = {}^6C_2 = 15$ (both odd). $P = \frac{10}{10 + 15} = \frac{10}{25} = \frac{2}{5}$.
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