Two dice are tossed, the probability that the total score is a prime number is

• Probability

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Answer : D. 5/12

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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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