An integer is chosen at random from the first 100 positive integers. What is the probability that the integer chosen is a prime or multiple of 8?
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An integer is chosen at random from the first 100 positive integers. What is the probability that the integer chosen is a prime or multiple of 8?
An integer is chosen at random from the first 100 positive integers. What is the probability that the integer chosen is a prime or multiple of 8?
S= {1, 2, 3, … 100}
n(S) = 100
Let A be the event of choosing a prime number
∴ A = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89}
n(A) = 25
So P(A) = 25/100
Let B be the event of getting a number multiple of 8
B = {8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96}
n(B)= 12
So P(B) = 12/100
Also A ∩ B = ϕ
⇒ A and B are mutually exclusive
∴ P(A ∪ B) = P(A) + P(B) = (25/100) + (12/100) = 37/100