Chapter 13.4, Problem 7PPS

To determine

To calculate:

The probability of given event.

Answer to Problem 7PPS

The probability event is $87.5\%$ .

Explanation of Solution

Given information:

Event:

Pilar is playing a board game with eight diffreent categories, each with questions that must be answered correctly in otder to win.

Calculation:

Pilar is playing a board game with eight diffreent categories, each with questions that must be answered correctly in otder to win. To simulate the outcomes, make a spinner with eight equal segments that represent probability that the probability is chosen.

Spin the spinner $40$ times and record the frequency of observed outcomes.

The frequency of outcomes will vary between sets of $40$ spines. One such set, of spines can be recorded in a frequency table as follows:

Outcome	Frequency
Category$1$	$5$
Category$2$	$5$
Category$3$	$4$
Category$4$	$5$
Category$5$	$6$
Category$6$	$3$
Category$7$	$6$
Category$8$	$6$
Total	$40$

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

Outcome	Frequency	Probability
Category$1$	$5$	$\frac{5}{40}=0.125$
Category$2$	$5$	$\frac{5}{40}=0.125$
Category$3$	$4$	$\frac{4}{40}=0.10$
Category$4$	$5$	$\frac{5}{40}=0.125$
Category$5$	$6$	$\frac{6}{40}=0.15$
Category$6$	$3$	$\frac{3}{40}=0.075$
Category$7$	$6$	$\frac{6}{40}=0.15$
Category$8$	$6$	$\frac{6}{40}=0.15$
Total	$40$	$\frac{40}{40}=1$

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

  

Hence, the probability that a certain one of the eight categories is necessary is selected is about $12.5\%$ , and the probability of not selecting that category is about,

  $100\%-12.5\%=87.5\%$

Therefore, the probability event is $87.5\%$ .