Example 22

EXAMPLE 22 Multiplication Rule

According to the Pew Internet and American Life Project,¹¹ 35% of American adults have cell phones with apps, but only 68% of those who have apps on their cell phones actually use the apps. Define the following events:

$A : American adult has a cell phone with apps.$
$U : American adult uses the apps on his or her cell phone.$

Find $P (A)$ .
Find $P$ ( $U$ given $A$ ), the probability that an American adult uses the apps, given that he or she has a cell phone with apps.
Use the multiplication rule to calculate $P (A and U)$ , the probability that an American adult has a cell phone with apps and uses the apps on his or her cell phone.

Solution

According to the study, 35% of American adults have a cell phone with apps. So $P (A)$ = 0.35.
The research says that 68% of those who have apps actually use them, so $P (U given A) = 0.68$ .
Using the Multiplication Rule, we have
$P (A and U) = P (A) \cdot P (U given A) = 0.35 (0.68) = 0.238$

The probability that an American adult has a cell phone with apps and uses them is 0.238.

NOW YOU CAN DO

Exercises 53–58.