Chapter 13.6, Problem 14PPS

To determine

To determine the probability.

Answer to Problem 14PPS

Probability is $\frac{168}{300}$ or 56%

Explanation of Solution

Given information :

  

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 a player of age 14 can play basketball, which is common to both events. Hence the events are not mutually exclusive.

Total players are 300.

Probability that a player is of age 14 is $\frac{106}{300}$ (there are 106 players of age 14)

Probability that a player plays basketball is $\frac{104}{300}$

Now,

P(age of 14 and play basketball) $=\frac{42}{300}$ (42 players are in common)

P(age of 14 or play basketball) $=\frac{106}{300}+\frac{104}{300}-\text{P(age 14 and play basketball)}$

P(age of 14 or play basketball) $=\frac{106}{300}+\frac{104}{300}-\frac{42}{300}=\frac{168}{300}$ or 56%