Question

The Pew Research Center asked a random sample of $2024$adult 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 $18to34$and does not own an iPhone?

b. The person is age $18to34$or owns an iPhone?

Short answer

Part a. Probability that the person not aged $18-34$and does not own iPhone is approx.$0.5973$.

Part b. Probability that the person aged $18-34$or owns an iPhone is approx. role="math" localid="1663232478435" $0.4027$.

Step-by-step solution

Part a. Step 1. Given information

Data summarized in two – way table:

Part a. Step 2. Explanation

The table consists of data about $2024$adult cell – phone users.

Thus,

The number of possible outcomes is $2024$.

Now,

The people not aged $18-34$and do not own iPhone are as follows:

Android users (other than aged $18-34$):

$189$adults aged $35-54$use Android.

$100$adults aged $55+$use Android.

Other cell – phone users (other than aged $18-34$):

$277$adults aged $35-54$use other cell – phones.

$643$adults aged $55+$use other cell – phones.

When we sum up all the above counts, it becomes $1209$.

That means

$1209$adults not aged $18-34$do not own an iPhone.

Thus,

The number of favorable outcomes is $1209$.

If we divide number of favorable outcomes by number of possible outcomes, we get the probability.

P(Not$18-34$) and do not own iphone)$$\begin{gathered} =\frac{Numberoffavorableoutcomes}{Numberofpossibleoutcomes} \\ =\frac{1209}{2024} \\ \approx 0.5973 \end{gathered}$$

Thus,

Probability for the person not aged $18-34$and does not own an iPhone is approx.$0.5973$

Part b. Step 1. Explanation

The table consists of data about $2024$adult cell – phone users.

Thus,

The number of possible outcomes is $2024$.

Now,

For people aged $18-34$or own an iPhone:

Aged $18-34$:

$517$of $2024$adults are aged $18-34$.

iPhone users (other than aged $18-34$):

$171$adults aged $35-54$use iPhone.

$127$adults aged $55+$use iPhone.

When we sum up all the above counts, it becomes $815$.

That means

$815$adults aged $18-34$or own an iPhone.

Thus,

The number of favorable outcomes is $815$.

If we divide number of favorable outcomes by number of possible outcomes, we get the probability.

P(Aged $18-34$) or own iphone)$$\begin{gathered} =\frac{Numberoffavorableoutcomes}{Numberofpossibleoutcomes} \\ =\frac{805}{2024} \\ \approx 0.4027 \end{gathered}$$

Thus,

Probability for the person aged $18-34$or owns an iPhone is approx.$0.4027$.