When two dice are tossed, What is the probability that the total score is a prime number ?



When two dice are tossed, What is the probability that the total score is a prime number ?

A. 1/4

B. 1/3

C. 2/3

D. 5/12

Answer : D. 5/12


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.
    Prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 … etc
    Let E = the event that the total is a prime number
               = {(1,1), (1,2), (1,4), (1,6), (2,1), (2,3), (2,5), (3,2), (3,4), (4,1), (4,3), (5,2), (5,6), (6,1), (6,5)}
    Hence, n(E) = 15
    P(E) = n(E)/n(S)
             = 15/36 = 5/12


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