According to Reuters, a survey undertaken by the National Center for Health Stat

Question

According to Reuters, a survey undertaken by the National Center for Health Statistics revealed that about 25% of U.S. households have only a cell phone (no land line). According to the FCC, 65% of U.S. households have high-speed Internet. Suppose of U.S. households having only a cell phone, 80% have high-speed Internet. A U.S. household is randomly selected.

(Round your answers to 2 decimal places.)

a. What is the probability that the household has only a cell phone and has high-speed Internet?

b. What is the probability that the household has only a cell phone or has high-speed Internet?

c. What is the probability that the household has only a cell phone and does not have high-speed Internet?

d. What is the probability that the household does not have just a cell phone and does not have high-speed Internet?

e. What is the probability that the household does not have just a cell phone and does have high-speed Internet?

Explanation / Answer

P(having only a cell phone) = 0.25

P(having high-speed Internet) = 0.65

P(having high-speed Internet | having only a cell phone) = 0.8

a) P(having high-speed Internet | having only a cell phone) = P(having high-speed Internet and having only a cell phone) / P(having only a cell phone)

or, 0.8 = P(having high-speed Internet and having only a cell phone) / 0.25

or, P(having high-speed Internet and having only a cell phone) = 0.2

b) P(having high-speed Internet or having only a cell phone) = P(having high-speed Internet) + P(having only a cell phone) - P(having high-speed Internet and having only a cell phone)

                                                                      = 0.25 + 0.65 - 0.2

                                                                      = 0.7

c) P(having only a cell phone) = P(having only a cell phone and having high-speed Internet) + P(having only a cell phone and not having high-speed Internet)

or, 0.25 = 0.2 + P(having only a cell phone and not having high-speed Internet)

or ,P(having only a cell phone and not having high-speed Internet) = 0.05

d) P(not having only a cell phone and not having high-speed Internet) = 1 - P(having high-speed Internet or having only a cell phone)

                                                                  = 1 - 0.7

                                                                  = 0.3

e) P(having high-speed Internet) = P(having high-speed Internet and having only a cell phone) + P(having high-speed Internet and not having only a cell phone)

or, 0.65 = 0.2 + P(having high-speed Internet and not having only a cell phone)

or, P(having high-speed Internet and not having only a cell phone) = 0.45

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