Thirty cards numbered 1 to 30 are put in a box and one card is drawn at random. Find the probability that the number on the card is:(a) a multiple of 3 or 5(b) a perfect square(c) a prime number.

Answer: (a) \(\dfrac{7}{15}\) (b) \(\dfrac{1}{6}\) (c) \(\dfrac{1}{3}\)

S = {1, 2, 3, …, 30}, n(S) = 30

(a) Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 (10). Multiples of 5: 5, 10, 15, 20, 25, 30 (6). 15 and 30 are in both lists, so count them once.

A = {3, 5, 6, 9, 10, 12, 15, 18, 20, 21, 24, 25, 27, 30}, n(A) = 10 + 6 − 2 = 14, \(P(A) = \dfrac{14}{30} = \dfrac{7}{15}\)

(b) B = {1, 4, 9, 16, 25}, n(B) = 5, \(P(B) = \dfrac{5}{30} = \dfrac{1}{6}\)

(c) C = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29}, n(C) = 10, \(P(C) = \dfrac{10}{30} = \dfrac{1}{3}\)