Question

39.4% of US homes continue to use a landline in addition to cell phone service. 3 US homes are randomly

selected. What is the probability that at least one of the 3 continues to use a landline? Round your answer
to 4 decimal places.

Answer 1

0.7787, or 77.87% chance

Step-by-step explanation:

To calculate the probability that at least one of the three randomly selected US homes continues to use a landline, we can calculate the complement of the event where none of the three homes uses a landline.

The probability that a single randomly selected US home does not use a landline is 1 - 0.394 = 0.606 (since 39.4% use a landline). Therefore, the probability that none of the three homes use a landline is (0.606)^3 = 0.2213.

To find the probability that at least one of the three homes uses a landline, we subtract the probability of none of them using a landline from 1:

P(at least one landline) = 1 - P(no landlines)

P(at least one landline) = 1 - 0.2213

P(at least one landline) ≈ 0.7787

Rounded to four decimal places, the probability that at least one of the three randomly selected US homes continues to use a landline is approximately 0.7787.