Ten tickets numbered 1 to 15 are placed in a box, mixed up thoroughly and then one ticket is drawn randomly. If it is known that the number on the drawn ticket is more than 3, what is the probability that it is an even number?
Let A be the event ‘the number on the ticket drawn is even’ and B be the event ‘the number on the ticket drawn is greater than 3’. We have to find P(A|B). Now, the sample space of the experiment is S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} Then A = {2, 4, 6, 8, 10, 12, 14}, B = {4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15} and A ∩ B = {4, 6, 8, 10, 12, 14} Also P(A) = 7/15, P(B) = 12/15 and P(A ∩ B) = 6/15 Then P(A|B) = P(A ∩ B)/P(B) = (6/15)/(12/15) = 1/2
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