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 divisible by 3 and 5?

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 D be the event that number on ticket is divisible by 3 and 5 i.e., divisible by L.C.M. of 3 and 5 i.e., 15
D = {15, 30, 45, 60, 75}
∴ n(D) = 5

∴ P(D) = `("n"("D"))/("n"("S")`

= `5/75`

= `1/15`