Chapter 13.4, Problem 8PPS

To determine

To calculate:

The probability of given event.

Answer to Problem 8PPS

The probability that a movie ticket sale is for a drama is $50\%$ , for mystery is $20\%$ , for comedy is $30\%$ , and for an Action is $0\%$ .

Explanation of Solution

Given information:

Event:

A movie theater reviewed sales from the privious year to determine which genre of movie sold the most tickets. The results are as shown at the below.

Genre	Ticket $\%$
Drama	$40\%$
Mystery	$30\%$
Comedy	$25\%$
Action	$5\%$

Calculation:

To simulate the movie ticket sales and estiamate the probability that a ticket will be sold from each genre, use a random number generator to generate integers from $1-20$ .

Generate $20$ integers, and let the integers from $1-8$ represent the $D$ genre, let integers $9-14$ represent $M$ .

Now let integers $15-19$ represent $C$ and $20$ represent $A$ .

Record the frequency of observed outcomes. The frequency of observed outcomes. The frequency of outcomes will vary between sets of $20$ integers.

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

Genre	Frequency
Drama	$10$
Mystery	$4$
Comedy	$6$
Action	$0$
Total	$20$

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

Genre	Frequency	Probability
Drama	$10$	$\frac{10}{20}=0.50$
Mystery	$4$	$\frac{4}{20}=0.20$
Comedy	$6$	$\frac{6}{20}=0.30$
Action	$0$	$\frac{0}{20}=0$
Total	$20$	$\frac{20}{20}=1$

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

  

Hence, based on the simulation, the probability that a movie ticket sale is for a drama is $50\%$ , for mystery is $20\%$ , for comedy is $30\%$ , and for an Action is $0\%$ .