Chapter 13.4, Problem 11PPS

To determine

To calculate:

The probability of given event.

Answer to Problem 11PPS

The probability that a car sold is of color $B$ is $32\%$ , for $R$ is $32\%$ , for $W$ is $16\%$ , $BI$ is $18\%$ , and $A$ is $2\%$ .

Explanation of Solution

Given information:

Event:

A car dealerships analysis insicated that $35\%$ of the customers purchased a blue car, $30\%$ purchased a red car, $15\%$ purchased a white car, $15\%$ purchased a black car, and $5\%$ purchased any other color.

Calculation:

The following table represents the percentage of colors of cars sold at a dealership.

Color	Percentage of Tickets
$B$	$35\%$
$R$	$30\%$
$W$	$15\%$
$BI$	$15\%$
$A$	$5\%$

To simulate car color sales, use a random number generator to generate integers from $1-20$ .

Generate $50$ integers, and let the integers from $1-7$ represent the $B$ , let integers $8-13$ represent $R$ .

Now let integers $14-16$ represent $W$ hit and let $17-19$ represent $BI$ and let $20$ represent. $A$ .

Record the frequency of observed outcomes. The frequency of observed outcomes. The frequency of outcomes will vary between sets of $50$ integers.

One such set of spins can be recorded in a frequency table as follows:

Outcome	Frequency
$B$	$16$
$R$	$16$
$W$	$8$
$BI$	$9$
$A$	$1$
Total	$50$

Now, divide each frequency in the frequency table to get the probabilities for each outcome.

Outcome	Frequency	Probability
$B$	$16$	$\frac{16}{50}=0.32$
$R$	$16$	$\frac{16}{50}=0.32$
$W$	$8$	$\frac{8}{50}=0.16$
$BI$	$9$	$\frac{9}{50}=0.18$
$A$	$1$	$\frac{1}{50}=0.02$
Total	$50$	$\frac{20}{20}=1$

Make a probability histogram by charting probability on the vertical axis and outcomes on the horizontal axis.

  

Therefore, based on the simulation, the probability that a car sold is of color $B$ is $32\%$ , for $R$ is $32\%$ , for $W$ is $16\%$ , $BI$ is $18\%$ , and $A$ is $2\%$ .