## A survey showed that 24% of college students read newspapers on a regular basis and that 82% of college students regularly watch the news on

Question

A survey showed that 24% of college students read newspapers on a regular basis and that 82% of college students regularly watch the news on TV. The survey also showed that 21% of college students both follow TV news regularly and read newspapers regularly.

(a) What is the probability that a student watches TV news regularly, given that he or she regularly reads newspapers? Round your answer to 2 decimal places.
(b) What is the probability that a randomly selected college student reads newspapers regularly, given that he or she watches TV news regularly? Round your answer to 2 decimal places.

in progress 0
4 weeks 2021-11-10T16:25:35+00:00 1 Answer 0 views 0

a) 0.88 = 88% probability that a student watches TV news regularly, given that he or she regularly reads newspapers.

b) 0.26 = 26% probability that a randomly selected college student reads newspapers regularly, given that he or she watches TV news regularly

Step-by-step explanation:

We solve this problem building the Venn’s diagram of these probabilities.

I am going to say that:

A is the probability that a college student read newspapers on a regular basis.

B is the probability that a college student regularly watch the news of TV.

We have that:

In which a is the probability that a students reads newspapers but does not watches TV and is the probability that a student does both of these things.

By the same logic, we have that:

The survey also showed that 21% of college students both follow TV news regularly and read newspapers regularly.

This means that

24% of college students read newspapers on a regular basis;

This means that .

82% of college students regularly watch the news on TV.

This means that

(a) What is the probability that a student watches TV news regularly, given that he or she regularly reads newspapers? Round your answer to 2 decimal places.

By the Bayes Rule, probability of event B, given that A, is given by the following formula.

So

0.88 = 88% probability that a student watches TV news regularly, given that he or she regularly reads newspapers.

(b) What is the probability that a randomly selected college student reads newspapers regularly, given that he or she watches TV news regularly? Round your answer to 2 decimal places.

By the Bayes Rule, probability of event A, given that B, is given by the following formula.

So

0.26 = 26% probability that a randomly selected college student reads newspapers regularly, given that he or she watches TV news regularly