Theory question 105
ProbabilityTwo fair dice are thrown. M is the event described by "the sum of the scores is 10" and N is the event described by "the difference between the scores is 3". (a) Write out the elements of M and N. (b) Find the probability of M or N. (c) Are M and N mutually exclusive? Give reasons.
Show the model answer
Model answer
(a) M = {(4, 6), (5, 5), (6, 4)}; N = {(1, 4), (4, 1), (2, 5), (5, 2), (3, 6), (6, 3)}.
(b) P(M) = 3/36, P(N) = 6/36. They share no outcome, so P(M or N) = 9/36 = 1/4.
(c) Yes. No pair of scores has sum 10 and difference 3, so M ∩ N = ∅ and they cannot happen together.
Explanation
Mutually exclusive events have no outcome in common.