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What is the probability of getting a sum of 22 or more when four dice are thrown?

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1456

5432

9756

1756

answer is B.

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Detailed Solution

When the four dice are rolled together, the total possible outcome is

64 = 1296

.
The arrangements where the sum is 22 or greater than 22 is given by,

The maximum possible sum is

6 + 6 + 6 + 6 = 24

The sum that can be obtained in 4 ways is

6 + 5 + 6 + 6 = 23

The sum that can be possible in 4 ways is

6 + 6 + 6 + 4 = 22

The sum that can be possible in 6 ways is

6 + 5 + 5 + 6 = 22

The total favourable outcome is

1 + 4 + 4 + 6 = 15

.
Then, the probability is,

= 151296 = 5432

Hence, the correct option is 2.

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