Question

An integers is chosen at random from the first fifty positive integers. What is probability that the integer chosen is a prime or multiple of 4.

Answer 1

S = {1, 2, 3, … ,50} 

∴ n(S) = 50 

Let A be the event of getting prime number. 

∴ A = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47}

n(A) = 15, so P(A) = 15/50 

Let B be the event of getting number multiple of 4 

∴ B = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48} 

n(B) = 12, so P(B) = 12/50 

Here A and B are mutually exclusive. (i.e.,) A ∩ B = ϕ 

∴ P(A ∪ B) = P(A) + P(B) = 15/50 + 12/50 = 27/50.