A number is selected from the set {1, 2, 3, … , 20}. The probability

1.	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» (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

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»

(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

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