Explanation

(a)
Given, one integer is chosen at random from the first 200 positive integers and integer chosen is divisible by 6 or 8.
$\therefore$ One integer can be chosen out of 200 integers in ${\ ^{200}C}_{1}$ ways.
Let $A$ be the event that an integer selected is divisible by 6 and $B$ that it is divisible by 8.
Then, $P(A) = \frac{33}{200},\ P(B) = \frac{25}{200}$
and $P(A \cap B) = \frac{8}{200}$
$\therefore P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$= \frac{33}{200} + \frac{25}{200} - \frac{8}{200} = \frac{1}{4}$