Chapter 13.6, Problem 9PPS

To determine

To determine whether the events are mutually exclusive or not mutually exclusive. Also find probability.

Answer to Problem 9PPS

Not mutually exclusive.

Probability is $\frac{10}{36}$ or 27.8%

Explanation of Solution

Given information :

Rolling a pair of dice and getting a doubles or a sum of 8

Two events can be mutually exclusive if there is no common outcome of the both events. Whereas if there is any common outcome then the events becomes not mutually exclusive events.

There is possibility that we get (4, 4) , this is a common outcome to both events hence they are not mutually exclusive events.

Total outcomes on rolling two dice is 36.

Probability of getting a double is $\frac{6}{36}=\frac{1}{6}$

(Favorable outcomes are (1, 1),(2, 2), (3,3), (4, 4), (5, 5), (6, 6))

Probability of getting a sum of 8 is $=\frac{5}{36}$

(Favorable outcomes are (2, 6), (3, 5), (4, 4), (5, 3), (6, 2))

Now probability of getting jack or six is,

P(doubles or sum of 8) $=\frac{1}{6}+\frac{5}{36}-\text{P(double and sum of 8)}$

Hence we get,

P(doubles or sum of 8) $=\frac{1}{6}+\frac{5}{36}-\frac{1}{36}=\frac{10}{36}$ or 27.8%