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# 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? - Mathematics and Statistics

Sum

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?

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#### Solution

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 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

Concept: Addition Theorem of Probability
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