Chapter 5.2, Problem 43E

(a)

To determine

Probability for the person not aged 18 − 34 and does not own an iPhone.

Answer to Problem 43E

Probability that the person not aged 18 − 34 and does not own iPhone is approx. 0.5973.

Explanation of Solution

Given information:

Data summarized in two − way table:

  

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.

  $\begin{array}{l}P\left(\text{Not}18-34\text{and}\text{do}\text{not}\text{own}\text{iPhone}\right)=\frac{\text{Number}\text{of}\text{favorable}\text{outcomes}}{\text{Number}\text{of}\text{possible}\text{outcomes}}\\ =\frac{1209}{2024}\\ \approx 0.5973\end{array}$

Thus,

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

(b)

To determine

Probability for the person aged 18 − 34 or owns an iPhone.

Answer to Problem 43E

Probability that the person aged 18 − 34 or owns an iPhone is approx. 0.4027.

Explanation of Solution

Given information:

Data summarized in two − way table:

  

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:

Aged18 − 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.

  $\begin{array}{l}P\left(\text{Aged}18-34\text{or}\text{own}\text{iPhone}\right)=\frac{\text{Number}\text{of}\text{favorable}\text{outcomes}}{\text{Number}\text{of}\text{possible}\text{outcomes}}\\ =\frac{805}{2024}\\ \approx 0.4027\end{array}$

Thus,

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