Two fair die are thrown. M is the event described by "The sum of the...

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 \(M \cap N = \emptyset\).