Question

39.4% of us continue to use a landline in addition to cell phone service. If 5 US homes are randomly selected, what is the probability that at least one of the 5 continues to use a landline?

A) 0.013
B) 0.686
C) 0.999
D) 0.313

Answer 1

The probability that at least one of the 5 homes uses a landline is calculated by finding the complementary probability that none use a landline, and then subtracting from 1. The correct option is B) 0.686.

Step-by-step explanation:

To find the probability that at least one of the 5 randomly selected US homes continues to use a landline when 39.4% of US homes use landlines, we look at the complementary event - the probability that none of the 5 homes use a landline. The probability that one specific home does not use a landline is 1 - 0.394 = 0.606. Because the homes are selected randomly, we assume that whether one home uses a landline is independent of another home's landline use.

We calculate the probability that none of the 5 homes uses a landline by raising the probability that one home does not use a landline to the fifth power: (0.606)^5. Once we have this probability, we subtract it from 1 to find the probability that at least one home uses a landline.

Performing the calculation, (0.606)^5 = 0.0876 approximately. Subsequently, 1 - 0.0876 = 0.9124. This result means there's a 91.24% chance that at least one of the selected homes uses a landline. Therefore, the answer closest to this computed probability from the given options is B) 0.686.