Two fair die 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.
Explanation
(a) M = {(4, 6), (5, 5), (6,4)}
N = {(1, 4), (2, 5), (3, 6), (4, 1), (5, 2), (6, 3)}
(b) Pr(M or N) = Pr(M) + Pr(N)
Total sample = 36.
\(Pr(M) = \frac{3}{36} = \frac{1}{12}\)
\(Pr(N) = \frac{6}{36} = \frac{1}{6}\)
\(Pr(\text{M or N}) = \frac{1}{12} + \frac{1}{6}\)
= \(\frac{2 + 1}{12}\)
= \(\frac{3}{12} = \frac{1}{4}\)
(c) Yes, they are mutually exclusive since \(M \cap N = \emptyset\).