Question

A bag contains 50 tickets, numbered from 1 to 50. One ticket is drawn at random. What is the probability that, number on the ticket is a prime number or greater than 30?

Answer 1

Out of the 50 tickets, a ticket can be drawn in ⁵⁰C₁ = 50 ways.
∴ n(S) = 50
Let A be the event that the number on the ticket is a prime number.
A = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47}
∴ n(C) = 15

∴ P(A) = `("n"("A"))/("n"("S")) = 15/50`
Let B be the event that the number is greater than 30.
∴ B = {31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50}
∴ n(B) = 20

∴ P(B) = `("n"("B"))/("n"("S")) = 20/50`

Now, A ∩ B = {31, 37, 41, 43, 47}
∴ n(A ∩ B) = 5

∴ P(A ∩ B) = `("n"("A" ∩  "B"))/("n"("S")) = 5/50`

∴ Required probability = P(A ∪ B)
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

= `15/50 + 20/50 - 5/10`

= `(15+20-5)/50`
= `3/5`