Question

A large cable company reports that 42% of its customers subscribe to its Internet service, 32% subscribe to its phone service and 23% subscribe to both its Internet service and phone service.

a) What is the probability that a randomly selected customer subscribes to the Internet service or the phone service?

b) What percent of customers subscribe to neither the Internet service nor the phone service?

Answer 1

P(A or B) = P(A) + P(B) - P(A & B)

P(internet service) = 0.42

P(phone service) = 0.32

P(both) = 0.23

a) P(a randomly selected customer subscribes to the Internet service or the phone service) = P(internet service) + P(phone service) - P(both)

= 0.42 + 0.32 - 0.23

= 0.51

b) P(a customer subscribes to neither the Internet service nor the phone service) = 1 - P(a customer subscribes to the Internet service or the phone service)

= 1 - 0.51

= 0.49

49% of customers subscribe to neither the Internet service nor the phone service