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Find the probability that the first roll is a total of at least 8 and the...

Find the probability that the first roll is a total of at least 8 and the second roll is a total of at least 4.

Math   Statistics-And-Probability   
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Answer #1

Probability = Favorable Outcomes / Total Outcomes.

In a roll of 2 dice, the total outcomes = 36

____________________________________________________________

* At least 8 = Sum of 8 + Sum of 9 + Sum of 10 + Sum of 11 + Sum of 12

= (2 6) (6 2) (3 5) (5 3) (4 4) (4 5) (5 4) (3 6) (6 3) (4 6) (6 4) (5 5) (5 6) (6 5) (6 6) = 15

Therefore the probability = 15/36 = 5/12

* At least 4 Sum of 4 till sum of 12 = Total cases - cases where sum is less than 4.

cases where sum is less than 4 = (1 1) (1 2) (2 1) =3 cases

There number of possibilities to get at least 4 = 36 - 3 = 33

The Probability = 33/36 = 11/12

Therefore the required probability = (5/12) * (11/12) = 55/144

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