Chapter 13.6, Problem 10PPS

To determine

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

Answer to Problem 10PPS

Not mutually exclusive.

Probability is $\frac{13}{20}$ or 65%

Explanation of Solution

Given information :

Selecting a number at random from integers 1 to 20 and getting a number divisible by 3.

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 3,6 . . etc , these are common outcome to both events hence they are not mutually exclusive events.

Total outcomes are 20.

Probability of selecting aeven number is $\frac{10}{20}=\frac{1}{2}$ (there are 10 even numbers between 1 to 20)

Probability of getting a number divisible by 3 is $\frac{6}{20}=\frac{3}{10}$

(Favorable outcomes are 3, 6, 9, 12, 15, 18)

Now P(even number and divisible by 3) $=\frac{3}{20}$ (common outcomes are 6, 12, 18)

Now probability of random number or number divisible by 3 is,

P(even number or divisible by 3) $=\frac{1}{2}+\frac{3}{10}-\text{P(even number and divisible by 3)}$

Hence we get,

P(even number or divisible by 3) $=\frac{1}{2}+\frac{3}{10}-\frac{3}{20}=\frac{13}{20}$ or 65%