Question

5)A national survey suggests that 25% of U.S. adults have a landline in their residence, 84% have a cell phone, and 21% have both. define the following: L= person has a landline in their residence, C= person has a cell phone. Answer the following questions using proper probability notation.

a) What is the probability that a randomly selected U.S. adult has a landline or a cell phone?

B)What is the probability that a randomly selected U.S. adult does not have a cell phone?

C)What is the probability that a randomly selected U.S adult has a cell phone but not a landline?

D) If a U.S. adult has a cell phone, what is the probability that he has a landline, too?

E) Are having a landline and a cell phone independent events? support your answer appropriately.

Answer 1

We are given :

P(L) = 25 % = 0.25

P(C) = 84% = 0.84

P(L and C) = 21% = 0.21

a)

Probability that a randomly selected U.S. adult has a landline or a cell phone = P(L) + P(C) - P(L and C)

= 0.25 + 0.84 - 0.21 = 0.88

b)

Probability that a randomly selected U.S. adult does not have a cell phone = 1 - P(C) = 1 - 0.84 = 0.16

c)

Probability that a randomly selected U.S adult has a cell phone but not a landline

= P(C) - P(L and C) = 0.84 - 0.21 = 0.63

d)

Probability that he has a landline given that U.S. adult has a cell phone = P(L | C ) = P(L and C) / P(C)

= 0.21 / 0.84 = 0.25

e)

Having a landline and a cell phone are independent events if :

P(L and C) = P(L)*P(C)

P(L)*P(C) = 0.25*0.84 = 0.21

Since, P(L)*P(C) = 0.21 and P(L and C ) = 0.21

Hence, Having a landline and a cell phone are independent events.