Q. A number is chosen at random among the first 120 natural numbers. The probability of the number chosen being a multiple of 5 or 15 is
A) $\frac{1}{8}$
B) $\frac{1}{5}$
C) $\frac{1}{24}$
D) $\frac{1}{6}$
Explanation
(b)
In first 120 natural number total number of multiple of 5, $n(A) = 24$ and total number of multiple of $15,\ n(B) = 8$ and $n(A \cap B) = 8$
$\therefore\ n(A \cup B) = n(A) + n(B) - n(A \cap B)$
$= 24 + 8 - 8 = 24$
$\therefore$ Required probability$= \frac{24}{120} = \frac{1}{5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.