Question

TV Location. The Television Bureau of Advertising publishes a report titled TV Basics for the purpose of providing information to help advertisers make the most effective and efficient use of local and national spot television advertisements. The following table gives a percentage distribution for the location of a television set in the home.

Suppose that a home television set is randomly selected. What is the probability that it is

(a) located in a bedroom?

(b) not located in a bedroom?

(c) located in the kitchen, dining room, basement, or garage?

Short answer

Part (a) 0.43

Part (b) 0.57

Part (c) 0.1

Step-by-step solution

Part (a) Step 1. Given information.

The given statement is:

The Television Bureau of Advertising publishes a report titled TV Basics for the purpose of providing information to help advertisers make the most effective and efficient use of local and national spot television advertisements.

The following table gives a percentage distribution for the location of a television set in the home.

Location	Percentage
Living or sitting room	27
Master bedroom	24
Child or other bedroom	19
Den or office	14
Kitchen or Dining room	5
Basement or Garage	5
Other room or Storage	6

Part (a) Step 2. Find the probability that the randomly selected TV is located in a bedroom.

Total percentage of TV Located in the bedroom:

24% in the master bedroom$+$19% in the child or other bedroom$=43\%$

role="math" localid="1651770355044" $$\begin{gathered} P(\mathrm{Television}\mathrm{in}\mathrm{bedroom})=43\% \\ =\frac{43}{100} \\ =0.43 \end{gathered}$$

Part (b) Step 1. Find the probability that the randomly selected TV is not located in a bedroom.

$$\begin{gathered} P(\mathrm{Television}\mathrm{not}\mathrm{located}\mathrm{in}\mathrm{bedroom})=1-P(\mathrm{Television}\mathrm{located}\mathrm{in}\mathrm{bedroom}) \\ =1-0.43 \\ =0.57 \end{gathered}$$

Part (c) Step 1. Find the probability that the randomly selected TV is located in the kitchen, dining room, basement, or garage.

The total percentage of TV Located in the kitchen, dining room, basement, or garage is:

5% in the kitchen or dining room$+$5% in the basement and garage$=10\%$

Therefore, the probability is:

$$\begin{gathered} =10\% \\ =0.1 \end{gathered}$$