An integer is chosen at random from the first 100 positive integers. W

1.	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?
Answer» 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

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?

Answer»

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

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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?

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