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Chapter 6: Problem 93

A theater complex is currently showing four R-rated movies, three \(\mathrm{PG}-13\) movies, two \(\mathrm{PG}\) movies, and one \(\mathrm{G}\) movie. The following table gives the number of people at the first showing of each movie on a certain Saturday: $$ \begin{array}{rlc} \text { Theater } & \text { Rating } & \begin{array}{l} \text { Number of } \\ \text { Viewers } \end{array} \\ \hline 1 & \mathrm{R} & 600 \\ 2 & \mathrm{PG}-13 & 420 \\ 3 & \mathrm{PG}-13 & 323 \\ 4 & \mathrm{R} & 196 \\ 5 & \mathrm{G} & 254 \\ 6 & \mathrm{PG} & 179 \\ 7 & \mathrm{PG}-13 & 114 \\ 8 & \mathrm{R} & 205 \\ 9 & \mathrm{R} & 139 \\ 10 & \mathrm{PG} & 87 \\ \hline \end{array} $$Suppose that a single one of these viewers is randomly selected. a. What is the probability that the selected individual saw a PG movie? b. What is the probability that the selected individual saw a PG or a PG-13 movie? c. What is the probability that the selected individual did not see an R movie?

Short Answer

Expert verified
a. The probability that a viewer watched a PG movie is approximately 0.066. b. The probability that a viewer watched a PG or PG-13 movie is approximately 0.332. c. The probability that a viewer did not watch an R-rated movie is approximately 0.556.

Step by step solution

01

Step 1.

First, calculate the total number of viewers by adding up all the viewers from each theater. This will give us the total possible outcomes.
02

Step 2.

Calculate the total number of viewers for each movie rating. For example, for the PG movie rating, sum up the viewers from Theater 6 and Theater 10. This will give the number of outcomes of a viewer selected at random having watched a PG movie.
03

Step 3.

To determine probability, divide the number of viewers for a certain movie rating (desired outcomes) by total number of viewers (total outcomes). For part a, divide the number of viewers for PG movies by the total number of viewers.
04

Step 4.

Repeat the calculations for each part of the problem: calculate the total viewers for PG and PG-13 movies, then divide by the total viewers for part b; calculate the total viewers for all non-R movies, then divide by the total viewers for part c.

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