Question

SamaraCom is a communications and media company. It operates in the field of wireless communications, cable TV, telephone, and Internet connectivity. A recent survey showed that 64% of the SamaraCom clients are subscribed to Internet service, 28% are TV customers, and 22% are subscribed to a bundle (both, Internet and TV services). a.​What is the probability that a client is subscribed to TV service or Internet? b.​What is the probability that a SamaraCom client is subscribed to neither TV service nor Internet? c.​Are the events of T = {TV service subscription} and I = {Internet service subscription} disjoint (or mutually exclusive)? Explain.

Answer 1

The probability that a client is subscribed to TV service or Internet is 70%. The probability that a SamaraCom client is subscribed to neither TV service nor Internet is 30%. The events of TV service subscription and Internet service subscription are mutually exclusive.

Step-by-step explanation:

a. To find the probability that a client is subscribed to TV service or Internet, we need to add the probabilities of the two events and subtract the probability of the intersection of the two events. Let's denote TV service subscription as T and Internet service subscription as I. The probability of TV service subscription is 0.28, the probability of Internet service subscription is 0.64, and the probability of both TV and Internet service subscription is 0.22. So, the probability that a client is subscribed to TV service or Internet can be calculated as: P(T or I) = P(T) + P(I) - P(T and I). Therefore, P(T or I) = 0.28 + 0.64 - 0.22 = 0.70 or 70%.

b. To find the probability that a SamaraCom client is subscribed to neither TV service nor Internet, we take the complement of the probability that a client is subscribed to TV service or Internet. The complement probability is equal to 1 minus the probability that a client is subscribed to TV service or Internet. So, P(neither TV nor Internet) = 1 - P(T or I). Therefore, P(neither TV nor Internet) = 1 - 0.70 = 0.30 or 30%.

c. The events of TV service subscription (T) and Internet service subscription (I) are mutually exclusive because they cannot occur at the same time. If a client is subscribed to TV service, they cannot be subscribed to Internet service, and vice versa. Therefore, the events T and I have no intersection, and they are disjoint or mutually exclusive.