Chapter 12.5, Problem 14PPS

To determine

To state whether the probability is dependent or independent and find the probability.

Answer to Problem 14PPS

The events are independent and the probability that Mr. Escobar was given a green sedan and then a gray sedan is $\frac{24}{841}\text{ or 2}\text{.9\%}$ .

Explanation of Solution

Given information:

The given statement is:

“A rental agency has $12$ white sedans, $8$ gray sedans, $6$ red sedans and $3$ green sedans for rent. Mr. Escobar rents a sedan, returns it because the radio is broken, and gets another sedan. Assuming the returned sedan remains in circulation, what is the probability that Mr. Escobar was given a green sedan and then a gray sedan?”

Formula used:

The following formula is used:

  $\text{Probability}=\frac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}$

Calculation :

The outcome of one event does not affect the outcome of the other because the sedan is replaced and is still in circulation, so they are independent events.

The probability can be calculated by:

  $\begin{array}{l}\text{P}\left(\text{green sedan}\right)=\frac{3}{29}\\ \text{P}\left(\text{gray sedan}\right)=\frac{8}{29}\\ \text{P}\left(\text{green sedan, gray sedan}\right)=\frac{3}{29}\times \frac{8}{29}\\ \text{P}\left(\text{green sedan, gray sedan}\right)=\frac{24}{841}\text{ or 2}\text{.9\%}\end{array}$

Hence, the events are independent and the probability that Mr. Escobar was given a green sedan and then a gray sedan is $\frac{24}{841}\text{ or 2}\text{.9\%}$ .