Question

From 1, 2, 3, …, 320 one number is selected at random. Find the probability that it is either a multiple of 7 or a multiple of 3.

(a) 72%

(b) 42.5%

(c) 12.8%

(d) 63.8%

This question was addressed to me by my school principal while I was bunking the class.

The origin of the question is Discrete Probability topic in portion Discrete Probability of Discrete Mathematics

Answer 1

The correct choice is (b) 42.5%

To elaborate: Number of multiples of 7=45 and number of multiples of 3=10^6 and number of numbers which are multiples of both 7 and 3 = 15 Thus, P (selecting either a multiple of 7 or a multiple of 3) = \(\frac{45}{320} + \frac{106}{320} – \frac{15}{320} = \frac{136}{320} = \frac{2}{5}\) = 0.425 or 42.5%.