ASK YOUR TEACHER According to a survey conducted in a certain year by the Federal Communications...

ASK YOUR TEACHER

According to a survey conducted in a certain year by the Federal Communications Commission (FCC) of 3005 adults who were home broadband users, 31.5% of those surveyed had switched their service over the past 3 years. Of those who had switched service in the past 3 years, 53% were very satisfied, 37% were somewhat satisfied, and 10% were not satisfied with their service. Of the 68.5% who had not switched service in the past 3 years, 46% were very satisfied, 43% were somewhat satisfied, and 11% were not satisfied with their service.

(a) What is the probability that a participant chosen at random had not switched service in the past 3 years and was very satisfied with their service?

(b) What is the probability that a participant chosen at random was not satisfied with their service?

Expert Solution

We are given here the total sample size as:
n = 3005 as the broadband users.

Also for probabilities we are given here that:
P( switched service in last 3 years) = 0.315

Also for those who switched, the conditional probabilities given here as:
P( very satisfied | switched service in last 3 years) = 0.53,
P( somewhat satisfied | switched service in last 3 years) = 0.37,
P( not satisfied | switched service in last 3 years) = 0.1

For those who did not switch, we are given the probabilities here as:
P( very satisfied | not switched service in last 3 years) = 0.46,
P( somewhat satisfied | not switched service in last 3 years) = 0.43,
P( not satisfied | not switched service in last 3 years) = 0.11

A) The probability that the user had not switched service over the last 3 years and was very satisfied is computed using Bayes theorem here as:

P( very satisfied and not switched service in last 3 years)
= P(not switched service in last 3 years)P( very satisfied | not switched service in last 3 years)
= 0.685*0.46
= 0.3151

Therefore 0.3151 is the required probability here.

B) Probability that a person chosen at random was not satisfied with the service is computed using addition law of probability here as:

P( not satisfied ) = P( not satisfied | switched service in last 3 years) P(switched service in last 3 years) + P(not satisfied | not switched service in last 3 years)P(not switched service in last 3 years)

P( not satisfied ) = 0.315*0.1 + 0.685*0.11 = 0.10685

Therefore 0.10685 is the required probability here.

orchestra answered 2 years ago

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