Consider a pair of fair. six-sided dice. For each of the following identify even

Question

Consider a pair of fair. six-sided dice. For each of the following identify events A and B. draw the appropriate Venn diagram, and calculate the requested probability. (a) What is the probability of getting two sixes on a roll of the dice? (b) What is the probability of getting a one or a two on a single roll of one die? (c) What is the probability of getting exactly one six on a roll of the dice? (d) What is the probability of getting at least one six on a roll of the dice? How is this answer related to answers (a) and (c)? (e) What is the probability that when one die comes up a six the other is a one?

Explanation / Answer

Probability that the two dice show the same number i.e., 6 = 6/36 =0.1667 Getting one or two on a single roll of a die is = (10/36) *(10/36) =0.0772 Probability that at least one six on a roll of a die = 11/36 = 0.3056 In (a) we get the same number i.e., 6 on two dice and in (C) we get at least one six on a roll of a die Probability of getting six on one die and the other is 1 is =2/36 = 0.0556

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