Question

8. In a small town, 58% of the households own a cellular phone, 34% own a pager, and 21% own both a cellular phone and a pager. (Hint: draw the Venn diagram) a. What is the probability that a randomly selected household owns a cellular phone or a pager? b. What is the probability that a randomly selected household owns cellular phone but not a pager? c. What is the conditional probability that a randomly selected household owns a pager given that the household owns a cellular phone?

Answer 1

a) P (owns cell phone or pager) = P(owns cell phone) + P(owns pager)- P(owns cell phone and pager) = 0.58 + 0.34- 0.21 = 0.71

P (owns cell phone or pager) = 0.71

b) P(owns cell phone only) = 0.37

c) P(owns pager / ows cell phone) = P( owns pager and cell phone) / P(owns cell phone)

P(A/B) = P(A $\cap$ B) / P(B)

P(owns pager / ows cell phone) = P( owns pager and cell phone) / P(owns cell phone) = 0.21 / 0.58 = 0.362

P(owns pager / ows cell phone) = 0.362