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
Answer & explanation
Correct answer: option 2
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 = $P(A ∪ B)$
$= P(A) +P(B) - P(A ∩ B)$
$=\frac{33}{200}+\frac{25}{200}-\frac{8}{192}=\frac{1}{4}$