Question

A number is selected from the set {1, 2, 3, … , 20}. The probability that the selected number is divisible by 3 or 4 is …

(a) 2/5

(b) 1/8

(c) 1/2

(d) 2/3

Answer 1

(c) 1/2

n(S) = 20 

A = {3, 6, 9, 12, 15, 18} ⇒ n(A) = 6

B = {4, 8, 12, 16, 20} ⇒ n(B) = 5 

A ∩ B = {12} ⇒ n(A ∩ B) = 1 

So P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

= (6/20) + (5/20) - (1/20) = 10/20 = 1/2