Question

A box contains 75 tickets numbered 1 to 75. A ticket is drawn at random from the box. What is the probability that, number on ticket is prime?

Answer 1

The box contains 75 tickets numbered 1 to 75.
∴ 1 ticket can be drawn from the box in ⁷⁵C₁ = 75 ways.
∴ n(S) = 75
Let C be the event that the number on the ticket is a prime number
∴ C = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73}

∴ n(C) = 21

∴ P(C) = `("n"("C"))/("n"("S")`

= `21/75`

= `7/25`