Chapter 13.6, Problem 13PPS

To determine

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

Answer to Problem 13PPS

Mutually exclusive.

Probability is $\frac{2}{9}$ or 22.2%

Explanation of Solution

Given information :

Rolling a pair of dice and getting a sum of either 6 or 10.

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.

Here in the given events there is no common outcome hence they are mutually exclusive.

Total outcomes are 36.

Probability of getting a sum of 6 is $\frac{5}{36}$

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

Probability of getting sum 10 is $\frac{3}{36}$

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

Now,

P(sum 6 or sum 8) $=\frac{5}{36}+\frac{3}{36}=\frac{8}{36}=\frac{2}{9}$ or 22.2%