Question

A large cable company reports the following. 80% of its customers subscribe to its cable TV service 38% of its customers subscribe to its Internet service 31% of its customers subscribe to its telephone service 23% of its customers subscribe to both its cable TV and Internet service 19% 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. Find and interpret the following probabilities.

(a) P(cable TV only) P(cable TV only) = _____._____% of cable company customers only subscribe to cable TV.

(b) P(Internet|cable TV) P(Internet|cable TV) = _____. Of the customers who subscribe to cable TV, % subscribe to Internet service.

(c) P(exactly two services) P(exactly two services) = _____._____ % of cable company customers subscribe to exactly two services (cable TV and Internet, cable TV and phone, or Internet and phone).

(d) P(Internet and cable TV only) P(Internet and cable TV only) = _____._____ % of cable company customers subscribe to Internet and cable TV only.

Answer 1

Answer:

Given,

a)

Probability of cable only = P(Cable) - P(cable and internet) - P(cable and telephone) + P(cable and internet and telephone)

= P(C) - P(C and I) - P(C and T) + P(C and I and T)

substitute given values

= 0.80 - 0.23 - 0.19 + 0.15

= 0.53

b)

P(Internet | cable) = P(I and C)/P(C)

substitute given values

= 0.23 / 0.80

= 0.2875

c)

P(exactly two services) = P(C and I) + P(C and T) + P(I and T) - P(C and I and T)

substitute given values

= 0.23 + 0.19 + 0.22 - 0.15

= 0.49

d)

P(Internet and cable only) = P(I and C) - P(I and C and T)

substitute given values

= 0.23 - 0.15

= 0.08