According to a survey conducted in a certain year by the Federal Communications Commission (FCC) of 3005 adults who were home broadband users, 34.5% of those surveyed had switched their service over the past 3 years. Of those who had switched service in the past 3 years, 51% were very satisfied, 39% were somewhat satisfied, and 10% were not satisfied with their service. Of the 65.5% who had not switched service in the past 3 years, 48% were very satisfied, 43% were somewhat satisfied, and 9% 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?

(a) The probability is 31.44%

(b) The probability is 9.345%

Step-by-step explanation:

The probability for part (a) is calculated as a multiplication of:

65.5% * 48% = 31.44%

Where 65.5% is the percentage of participants that had not switched service in the past 3 years and 48% are the percentage of those 65.5% that were very satisfy. So, the 31.44% of the participants had not switched service in the past 3 years and were very satisfied with their service.

Then, for part b, we have 2 cases:

Case 1: A person that had not had switched service in the past 3 years and was not satisfied with their service Case 2:A person that had not switch in the past 3 years and was not satisfied with their service.

So, the probability is calculated as a sum of these two probabilities.

Therefore, the probability for case 1 is calculated as:

34.5% * 10% = 3.45%

Where 34.5% is the percentage of participants that had switched service in the past 3 years and 10% are the percentage of those 34.5% that were not satisfy.

At the same way, the probability for case 2 is:

65.5% * 9% = 5.895%

Finally, the probability that a participant chosen at random was not satisfied with their service is the sum of 3.45% and 5.895%. That is:

3.45% + 5.895% = 9.345%