In a game of dice, you roll two standard six-sided dice and examine their sum.

a) What is the probability of rolling a 7? 1/6

b) If you roll the dice 20 times, what is the probability of rolling a total of 3 sums of 7?

c) How many times would you expect to roll the dice before you rolled a sum of 12? 36

Question

Moses

Mathematics

8 August, 19:37

In a game of dice, you roll two standard six-sided dice and examine their sum.

a) What is the probability of rolling a 7? 1/6

b) If you roll the dice 20 times, what is the probability of rolling a total of 3 sums of 7?

c) How many times would you expect to roll the dice before you rolled a sum of 12? 36

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Answers (1)

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Kathleen · Answer 1

Possible outcome of sum = 7 are: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1) = 6/6^2 = 1/6

Let X be a binomial distribution representing the number of sums of 7 obtained

P (X = 3) = 20C3 (1/6) ^17 (5/6) ^3 = 3.9 x 10^-11

You will roll the dice 36 times to obtain a sum of 12.