Q. An integer is chosen at random from first two hundred numbers. Then, the probability that the integer chosen is divisible by 6 or 8 is
A) $\frac{1}{4}$
B) $\frac{2}{4}$
C) $\frac{3}{4}$
D) None of these
Explanation
(a)
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 $P(A \cap B) = \frac{8}{200}$
$\therefore P(A \cup B) = P(A) + P(B) - P(A \cap B)$
$= \frac{33}{200} + \frac{25}{200} - \frac{8}{200} = \frac{1}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.