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 :

Question

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) (2/5) (B) (1/2) (C) (3/5) (D) (7/10)

Tardigrade Admin · Accepted Answer

Since sum of two numbers is even so either both are odd or both are even. Hence number of elements in reduced samples space = 5C2 + 6C2 so required probability = (5C2/5C2 + 6C2)

Q. 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 :

$\frac{2}{5}$

$\frac{1}{2}$

$\frac{3}{5}$

$\frac{7}{10}$

Since sum of two numbers is even so either both are odd or both are even. Hence number of elements in reduced samples space
$=^{5} C_{2} +^{6} C_{2}$
so required probability = $\frac{^{5} C _{2}}{^{5} C _{2} + ^{6} C _{2}}$