Chapter 13.4, Problem 6PPS

To determine

To calculate:

The probability of given event.

Answer to Problem 6PPS

The probability event is $90\%$ .

Explanation of Solution

Given information:

Event:

Kadisha is listening to a $CD$ with her $CD$ player set on the random mode. There are $10$ songs on the $CD$ .

Calculation:

Kadisha is listening to a $CD$ with her $CD$ player set on the random mode. There are $10$ songs on the $CD$ . To simulate the outcomes, make a spinner with ten segments that represent probability that a song is chosen.

Spin the spinner $20$ times and record the frequency of observed outcomes.

The frequency of outcomes will vary between sets of $20$ spines. One such set, of spines can be recorded in a frequency table as follows:

Outcome	Frequency
Song $1$	$2$
Song $2$	$2$
Song $3$	$1$
Song $4$	$2$
Song $5$	$3$
Song $6$	$2$
Song $7$	$2$
Song $8$	$2$
Song $9$	$2$
Song $10$	$2$
Total	$20$

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

Outcome	Frequency	Probability
Song $1$	$2$	$\frac{2}{20}=0.10$
Song $2$	$2$	$\frac{2}{20}=0.10$
Song $3$	$1$	$\frac{1}{20}=0.05$
Song $4$	$2$	$\frac{2}{20}=0.10$
Song $5$	$3$	$\frac{3}{20}=0.15$
Song $6$	$2$	$\frac{2}{20}=0.10$
Song $7$	$2$	$\frac{2}{20}=0.10$
Song $8$	$2$	$\frac{2}{20}=0.10$
Song $9$	$2$	$\frac{2}{20}=0.10$
Song $10$	$2$	$\frac{2}{20}=0.10$
Total	$20$	$\frac{20}{20}=1$

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

  

Hence, therefore probability that a certain one of the ten songs played is about $10\%$ , and the probability of not playing that specific song is about

  $100\%-10\%=90\%$

Therefore, the probability event is $90\%$ .