EXAMPLE 22 Multiplication Rule

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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:

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

Solution

  1. According to the study, 35% of American adults have a cell phone with apps. So = 0.35.
  2. The research says that 68% of those who have apps actually use them, so .
  3. Using the Multiplication Rule, we have

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.