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Chapter 5: Q. 43 (page 327)

Cell phonesThe Pew Research Center asked a random sample of 2024adult cell-phone owners from the United States their age and which type of cell phone they own: iPhone, Android, or other (including non-smartphones). The two-way table summarizes the data.

Suppose we select one of the survey respondents at random. What’s the probability that:

a. The person is not age 18to 34and does not own an iPhone?

b. The person is age 18to 34or owns an iPhone?

Short Answer

Expert verified

a. The probability of a person who is not between the ages of 18and 34and does not own an iPhone is approximately 0.5973.

b. The probability of someone between the ages of 18and 34owning an iPhone is approximately 0.4027

Step by step solution

01

Part (a) Step 1 : Given Information

We have to determine the probability for the person not aged 18 − 34 and does not own an iPhone.

02

Part (a) Step 2 : Simplification

A total of 2024adult cell phone users are shown in the table.
Thus,

2024is the maximum number of possible outcomes.

Now,
The following are the people who are not between the ages of 18and34 and do not own an iPhone:
Android users (other than those between the ages of 18and34):
Android is used by 189individuals aged 35to 54.
Android is used by 100persons aged55and up.
Other cell phone users (not under the age of18):
Other cell phones are used by 277adults aged 35to 54.
Other cell phones are used by 643individuals aged 55and up.
When all of the above counts are added together, we get 1209.
That is to say,
adults between the ages of 18and 34do not have an iPhone.
Thus,
The total number of positive outcomes is 1209.

The probability is calculated by dividing the number of favourable outcomes by the total number of possible possibilities.

P(Not 18 − 34 and do not own iPhone)=Number of favorable outcomesNumber of possible outcomes                                                                                =12092024     ≈0.5973
As a result, the probability of a person who is not between the ages of 18and 34and does not own an iPhone is approximately 0.5973.

03

Part (b) Step 1 : Given Information

We have to determine the probability for the person aged 18-34or owns an iPhone.

04

Part (b) Step 2 : Simplification

A total of 2024adult cell phone users are shown in the table.
Thus,
2024is the maximum number of possible outcomes.
Now,
For those between the ages of 18and34who own an iPhone:
18to 34years old:
517of the 2024adults are between the ages of 18and 34.
iPhone users (other than those between the ages of 18and 34):
iPhone is used by 171individuals aged 35to 54.
iPhone is used by 127individuals aged 55and up.
When all of the above counts are added together, the total is 815.
That is to say,
815adults between the ages of 18and 34own an iPhone.
Thus,
The total number of positive outcomes is815.

The probability is calculated by dividing the number of favourable outcomes by the total number of possible possibilities.

P(Aged 18 − 34 or own iPhone)=Number of favorable outcomesNumber of possible outcomes                                                                  =8052024    ≈0.4027

Thus,
The probability of someone between the ages of 18and 34owning an iPhone is approximately 0.4027.

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