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A fair die is rolled three times. Find the probability that one or more fours appear...

A fair die is rolled three times. Find the probability that one or more fours appear given that the sum of the three numbers that appear is 8.

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Answer #1

A fair die is rolled three times. Find the probability that one or more fours appear given that the sum of the three numbers that appear is 8.

Solution:

The numbers of ways that one or more fours appear given that the sum of the three numbers that appear is 8 are given as below:

(4,1,3)

(4,2,2)

(4,3,1)

(1,4,3)

(2,4,2)

(3,4,1)

(3,1,4)

(2,2,4)

(1,3,4)

So, there are total 9 ways that one or more fours appear given that the sum of the three numbers that appear is 8.

Total number of favourable outcomes = 9

Total number of outcomes = 6*6*6 = 216

Required probability = 9/216 = 0.041667

Required probability = 0.041667

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