Suppose that a student rolls two balanced dice three times i

Suppose that a student rolls two balanced dice three times in a row. What is the probability that on each of the three rolls, the sum of the two numbers that appears is 7?

Solution

There are 6*6 = 36 possibilities for each roll of 2 dice.

There are 6 ways to produce a 7, namely

1,6
2,5
3,4
4,3
5,2
6,1

Thus,

P(7 as sum) = 6/36 = 1/6

Thus, the probability that all 3 rolls are 7 is

P(all 3 rolls are 7) = (1/6)(1/6)(1/6)

= 1/216 [ANSWER]