7. Let $a, b, c$ be three, not necessarily distinct, numbers chosen randomly form the set $\{3,4,5,6,7,8\}$. Find the probability that $a b+c$ is even.
(ans. 0.5.
$\operatorname{Prob}(a b+c$ is even $)=\frac{4(3 \cdot 3 \cdot 3)}{6 \cdot 6 \cdot 6}=\frac{4}{8}$. This is because $(a b+c$ even $)$ iff ( $a b$ and $c$ even OR $a b$ and $c$ odd) iff ( $a, b, c$ even OR $a$ odd and $b, c$ even OR $b$ odd and $a, c$ even OR $a, b, c$ odd). These are disjoint events each with probability $\frac{3 \cdot 3 \cdot 3}{6 \cdot 6 \cdot 6}$.)