Question

A box contains cards numbered 3, 5, 7, 9, … 35, 37. A card is drawn at random from the box. Find the probability that the drawn card have either multiples of 7 or a prime number.

Answer 1

Sample space = {3, 5, 7, 9, ... 35, 37}

n(S) = 18

Let A be the event of getting a multiple of 7

A = {7, 21, 35}

n(A) = 3

P(A) = `("n"("A"))/("n"("S")) = 3/18`

Let B be the event of getting a prime number

B = {3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37}

n(B) = 11

P(B) = `("n"("B"))/("n"("S")) = 11/18`

A ∩ B = {7}

n(A ∩ B) = 1

P(A ∩ B) = `("n"("A" ∩ "B"))/("n"("S")) = 1/18`

P(A ∪ B) = P(A) + P(B) − P(A ∩ B) 

= `3/18 + 11/18 - 1/18`

= `(3 + 11 - 1)/18`

= `13/18`

Probability of getting a multiple of 7 or a prime number = `13/18`