A large cable company reports the following.

80% of its customers subscribe to its cable TV service.
41% of its customers subscribe to its Internet service.
31% of its customers subscribe to its telephone service.
25% of its customers subscribe to both its cable TV and Internet service.
20% of its customers subscribe to both its cable TV and phone service.
22% of its customers subscribe to both its Internet and phone service.
15% of its customers subscribe to all three services.

Consider the chance experiment that consists of selecting one of the cable company customers at random. Use the probability formulas of this section to find the following probabilities.

a. P(cable TV only)
b. P(Internet I cable TV)
c. P(exactly two services)
d. P(lnternet and cable TV only)

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abidemiokin abidemiokin · Answer 1 · 2020-10-19T19:24:31+02:00

Answer:

Step-by-step explanation:

Let n(U) be total amount or customers = 100%

n(C) = 80% of its customers subscribe to its cable TV service.

n(I) = 41% of its customers subscribe to its Internet service.

n(T) = 31% of its customers subscribe to its telephone service.

n(CnI) = 25% of its customers subscribe to both its cable TV and Internet service.

n(CnT) = 20% of its customers subscribe to both its cable TV and phone service.

n(InT) = 22% of its customers subscribe to both its Internet and phone service.

n(CnInT) = 15% of its customers subscribe to all three services

number of those that subscribed to TV only = n(C) - (n(CnInT')+(n(CnI'nT)+(n(CnInT))

= 80-[(25-15)+(20-15)+15]

= 80-{10+5+15)

= 80-30

= 50

Hence 50% read cable TV only

Pr(cable TV only) = 50/100 = 1/2

2) number of people that read internet and cable TV = 25%

Pr(internet and cable) = 25/100 = 1/4

3) number of people that had exactly two services are;

n(cable and internet only)+n(internet and phone only)+(cable and phone only)

= (25-15)+(22-15)+(20-15)

= 10+7+4

= 21%

Hence 21℅ read exactly two services

pr(exactly 2 services) = 21/100

4) number of people that read internet and cable only = n(CnI) - n(CnInP)

= 25-15 = 10%

Pr(Internet and cable only) = 10/100 = 1/10