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Question

Two dice are rolled.

If both dices have six faces numbered 1,2,3,5,7 and 11, then the probability that the sum of the numbers on the top faces is less than or equal to 8 is


A

1736

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B

49

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C

512

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D

12

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Solution

The correct option is A

1736


Explanation for the correct answer:

Two dice are rolled.

The total number of outcomes in sample space nS are given as

nS=62=36

The numbers on the faces of the dice are 1,2,3,5,7,11

The possible scenarios where the sum of the digits is less than or equal to eight is with the combination of 1,2,1,3,1,5,1,7,2,3,2,5,3,5

Hence the ordered pairs with the combination of these digits are 1,1,1,2,1,3,1,5,1,7,2,1,2,2,2,3,2,5,3,1,3,2,3,3,3,5,5,15,25,3,7,1

Number of ordered pairs =17

Hence the requiredprobability=NumberoforderedpairsnS

requiredprobability=1736

Hence, the probability of the sum of the digits appearing on the faces of the dice less than or equal to eight is 1736.

Hence, option A is the correct answer.


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