## 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

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.

## Answers ( )

Answer: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 regularlyStep-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