Maharashtra State BoardHSC Commerce 11th
Advertisement Remove all ads

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?

Advertisement Remove all ads

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
  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×