Chapter 13.6, Problem 8PPS

To determine

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

Answer to Problem 8PPS

Mutually exclusive.

Probability is $\frac{2}{13}$ or 15.4%

Explanation of Solution

Given information :

Drawing a card from a standard deck and getting a jack or a six.

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.

After drawing a card, we can either get a jack or a six. Hence the event cannot occur on the same time therefore the are mutually exclusive.

Probability of getting a jack $=\frac{4}{52}=\frac{1}{13}$

Probability of getting a six $=\frac{4}{52}=\frac{1}{13}$

Now probability of getting jack or six is,

P(jack or six) $=\frac{1}{13}+\frac{1}{13}=\frac{2}{13}$ or 15.4%