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You are rolling two 6-sided dice and examining the sum of the two dice (for example, if you roll a 3 and a 5, this is an 8).

a) What is the probability of rolling a sum of 7?
b) What is the probability of rolling a sum of 11?
c) What is the probability of rolling a sum of 7 or 11?
d) What is the probability of rolling a sum of 7 and 11?

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a)
Possibilities of the sum being 7:
1 + 6; 2+5 ; 3 + 4 ; 6 + 1 ; 4 + 3 ; 5 + 2
= 6
Total possible outcomes = 36
Probability of sum being 7 = 6/36 = 1/6

b)
Possibilities of sum being 11:
5 + 6 ; 6 + 5
= 2
Probability of sum being 11 = 2/36 = 1/18

c)
We add the probabilities:
1/6 + 1/18 = 4/18 = 2/9

d)
We now multiply by the probabilities:
1/6 x 1/18 = 1/108

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