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Two dice are tossed. The probability that the total score is a prime number is ?
3/5
7/9
1/2
5/12
1/6
3/5
7/9
1/2
5/12
1/6
Solution
The total number of outcomes when two dices are tossed is
= 62 = 36
Let, the total score be = S
2 ≤ S ≥ 12
Prime numbers in this range are: 2, 3, 5, 7 and 11.
The number of ways in which we can get sum as 2:
(1, 1) = 1 way
The number of ways in which we can get sum as 3:
(1, 2) and (2, 1) = 2 ways
The number of ways in which we can get sum as 5:
(1,4), (2, 3), (3, 2) and (4, 1) = 4 ways
The number of ways in which we can get sum as 7:
(1,6), (2, 5), (3, 4), (4, 3), (5, 2) and (6, 1) = 6 ways
The number of ways in which we can get sum as 7:
(5, 6) and (6, 5) = 2 ways
Total number of ways of getting a prime number is
= 1 + 2 + 4 + 6 + 2 = 15
Required probability = 15/36 = 5/12
