Question

4.20. According to a report released by the National Center for Health Statistics, 51% of U.S. households has only cell phones (no land line). According to the FCC, nearly 70% of the U.S. households have high-speed Internet. Suppose of the U.S. households having only cell phones, 80% have high-speed Internet. A U.S household is randomly selected. a. What is the probability that the household has only cell phones and has high-speed Internet

Answer 1

The probability that the household has only cell phones and has high-speed Internet is 0.408

Explanation:

Let A be the event that represents U.S. households has only cell phones

Let B be the event that represents U.S. households have high-speed Internet.

We are given that 51% of U.S. households has only cell phones

P(A)=0.51

We are given that 70% of the U.S. households have high-speed Internet.

P(B)=0.7

We are given that U.S. households having only cell phones, 80% have high-speed Internet. A U.S household is randomly selected.

P(B|A)=0.8

`(P(A\capB))/(P(A))=0.8\\P(A\capB)=0.8 * P(A)\\P(A\capB)=0.8 * 0.51\\P(A\capB)=0.408`

Hence the probability that the household has only cell phones and has high-speed Internet is 0.408