Question

If a television service subscriber has cable service, there is a 0.24 probability the subscriber has a DVR player. If the subscriber does not have cable service (e.g., has satellite service), there is a 0.7 probability the subscriber has a DVR player. Assume 75% of subscribers have cable service and answer the following for a randomly selected television service subscriber: If the subscriber does not have a DVR player, what is the probability the subscriber has cable service

Answer 1

Answer:

0.1163

Step-by-step explanation:

given that if a television service subscriber has cable service, there is a 0.24 probability the subscriber has a DVR player. If the subscriber does not have cable service (e.g., has satellite service), there is a 0.7 probability the subscriber has a DVR player

Let A1 be the event subscriber has cable service and A2  subscriber does not have cable service

A1 and A2 are mutually exclusive and exhaustive

P(A1) = 0.75, P(A2) = 0.25

B = Subscriber has a DVD player

P(B/A1) =0.24 and P(B/A2) = 0.7

Prob for the subscriber does not have a DVR player

= P(B') = P(A1B')+P(A2B') $= 0.75*(1-0.24)+0.25(1-0.7)\\= 0.57+0.075=0.645$

required probability = P(A2/B') = P(A2B')/P(B)

=$\frac{0.075}{0.645} \\=0.1163$