An integer is chosen at random from the first 200 positive integers. The probability that the integer chosen is divisible by 6 or 8 is

$\frac{1}{4}$

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 $P(A ∩ B) =\frac{8}{192}$

∴ Required probability = $P(A ∪ B)$

$= P(A) +P(B) -  P(A ∩ B)$

$=\frac{33}{200}+\frac{25}{200}-\frac{8}{192}=\frac{1}{4}$