Two integers selected at random from 1,,11.

Question

Two integers selected at random from $\{1,\dots,11\}$. Given the sum is even, find the conditional probability both are even.

Accepted Answer

$P(\text{sum even}) \propto {}^6C_2+{}^5C_2 = 15+10=25$; $P(\text{both even}) \propto {}^5C_2=10$.

$$P = \frac{10}{25}=\frac25$$

Solutions · 1