Chapter 13.3, Problem 52AYU

To determine

To calculate: The probability that a U.S. household does not own a pet when there was a $68$% probability that a U.S. household owns a pet.

Answer to Problem 52AYU

Solution:

The probability that a U.S. household does not own a pet is $0.32$.

Explanation of Solution

Given information:

According to the American Pet Products Manufacturers Association’s $2017-2018$ National Pet Owners Survey, there was a $68$% probability that a U.S. household owns a pet.

Formula used:

If $E$ represents any event and $\overline{E}$ represents the complement of event $E$, then the probability of complement event is,

$P(\overline{E})=1-P(E)$

Calculation:

Let, event $E$ denote a U.S. household owns a pet.

And, event $\overline{E}$ denotes a U.S. household does not own a pet.

Since, $68$% probability that a U.S. household owns a pet so, convert this $68$% in proportion.

That is, $P\left(E\right)=\frac{68}{100}=0.68$

Using theformula for probability of complement of an event, $P\left(\overline{E}\right)=1-P\left(E\right)$.

Hence, $P\left(\overline{E}\right)=1-0.68$

$\Rightarrow P\left(\overline{E}\right)=0.32$

Therefore, the probability that a U.S. household does not own a pet is $0.32$.