Question

Two integers are selected at random from integers $1$ to $11.$ If the sum is even. find the probability that both the numbers are (i) odd (ii) even

Answer 1

The odd numbers$=1,3,5,7,9,11$

The even numbers$=2,4,6,8,10$

Probability of selecting two odd numbers $=\frac{6C_2}{11C_2}=\frac{6\times 5}{11\times 10}=\frac{3}{11}$

Probability of selecting two even numbers$=\frac{5C_2}{11C_2}=\frac{5\times 4}{11\times 10}=\frac{2}{11}$.