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

9514 1404 393

Answer:

a) 51%

b) 49%

Explanation:

a) P(A∪B) = P(A) +P(B) - P(A∩B)

P(A∪B) = 42% +32% -23% = 74% -23% = 51%

51% subscribe to one or the other.

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b) P(¬A∩¬B) = P(¬(A∪B)) = 1 -P(A∪B) = 1 -51% = 49%

49% of customers subscribe to neither service.