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 perfect square or divisible by 4?

#### Solution

Out of the 50 tickets, a ticket can be drawn in ^{50}C_{1} = 50 ways

∴ n(S) = 50

Let A be the event that the number on the ticket is a perfect square.

A = {1, 4, 9, 16, 25, 36, 49}

∴ n(A) = 7

∴ P(A) = `("n"("A"))/("n"("S")) = 7/50`

Let B be the event that the number on the ticket is divisible by 4.

B = {4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48}

∴ n(B) = 12

∴ P(B) = `("n"("B"))/("n"("S")) = 12/50`

Now, A ∩ B = {4, 16, 36}

∴ n(A ∩ B) = 3

∴ P(A ∩ B) = `("n"("A" ∩ "B"))/("n"("S")) = 3/50`

∴ Required probability = P(A ∪ B)

P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

= `7/50 + 12/50 - 3/50`

= `16/50`

= `8/25`