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Question

If two dice are rolled simultaneously , then what is the probability that the sum of numbers is a multiple of either 2 or 7?

A
23
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B
2336
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C
1118
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D
712
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Solution

The correct option is A 23
Total number of outcomes = 36

Outcomes where the sum of numbers is a multiple of 2
= {(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (2, 6), (3, 1), (3, 3), (3, 5), (4, 2), (4, 4), (4, 6), (5, 1), (5, 3), (5, 5), (6, 2), (6, 4), (6, 6).

Outcomes where the sum of numbers is a multiple of 7 = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)}

Total number of favourable outcomes = 18+6 = 24

For an event E,Probability P(E)=Number of outcomes favourable to ENumber of all possible outcomes of the experiment

P(sum of numbers is multiple of either 2 or 7 ) =2436=23

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