Three fair dice are thrown. If you know that one and only one shows 4, what...

Three fair dice are thrown. If you know that one and only one shows 4, what is
the probability that the sum is 10.

Solutions

Expert Solution

total number of outcomes when two dice are thrown = 6 x 6

Total number of outcomes when three dice thrown = 6 x6 x6

When you know that one and only one shows 4, Number of possible outcomes = 6 x 6 = 36 (4 on one of the dices is fixed)

When you know that one die is showing 4 and the sum of three dice to be 10 then sum of the other dice to be 6

Outcomes: that the favor the sum of other two dice is 6 : (1,5),(2,4),(3,3),(4,2),(5,1)

Number of outcomes that favor the sum of the other two dice is 6 = 5

Therefore,

When three fair dice are thrown

When you know that one and only one shows 4, Number of outcomes that favor the sum of three dice to be 10 = 5

When you know that one and only one shows 4, Number of possible outcomes = 6 x 6 = 36

If you know that one and only one shows 4, the probability that the sum is 10

= When you know that one and only one shows 4, Number of outcomes that favor the sum of three dice to be 10 /

When you know that one and only one shows 4, Number of possible outcomes

= 5/36

If you know that one and only one shows 4, the probability that the sum is 10 = 5/36

orchestra answered 2 years ago

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