Two dice are rolled together. What is the probability of getting two numbers whose product is even ?



Two dice are rolled together. What is the probability of getting two numbers whose product is even ?

A. 17/36

B. 1/3

C. 3/4

D. 11/25

Answer : C. 3/4


Explanation:


    Total number of outcomes possible when a die is rolled = 6 (∵ any one face out of the 6 faces).
    Hence, Total number of outcomes possible when two dice are rolled, n(S) = 6 × 6 = 36.
    Let E = the event of getting two numbers whose product is even.
              = {(1,2), (1,4), (1,6), (2,1), (2,2), (2,3), (2,4), (2,5), (2,6), (3,2), (3,4), (3,6), (4,1), (4,2), (4,3), (4,4), (4,5), (4,6), (5,2),(5,4), (5,6), (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

    Hence, n(E) = 27
    P(E) = n(E) / n(S)
    = 27/36
    = 3/4


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