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    Question

    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?
    A 1/3 Correct Answer Incorrect Answer
    B 1/7 Correct Answer Incorrect Answer
    C 1/2 Correct Answer Incorrect Answer
    D 1/4 Correct Answer Incorrect Answer

    Solution

    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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