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A survey showed that 25% of college students read newspapers on a regular basis and that 81% 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.Answer the questions below. (If necessary, consult a list of formulas.)(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.

Question

A survey showed that 25% of college students read newspapers on a regular basis and that 81% 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.Answer the questions below. (If necessary, consult a list of formulas.)(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.

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Solution

(a) The probability that a student watches TV news regularly, given that he or she regularly reads newspapers, is calculated by finding the probability of both events happening (students who both watch TV news and read newspapers regularly) divided by the probability of the given event (students who read newspapers regularly).

The probability of both events happening is 21% or 0.21. The probability of the given event (students who read newspapers regularly) is 25% or 0.25.

So, the calculation is 0.21 / 0.25 = 0.84 or 84%. Rounded to two decimal places, the probability is 0.84.

(b) The probability that a randomly selected college student reads newspapers regularly, given that he or she watches TV news regularly, is calculated by finding the probability of both events happening (students who both watch TV news and read newspapers regularly) divided by the probability of the given event (students who watch TV news regularly).

The probability of both events happening is 21% or 0.21. The probability of the given event (students who watch TV news regularly) is 81% or 0.81.

So, the calculation is 0.21 / 0.81 = 0.259 or 25.9%. Rounded to two decimal places, the probability is 0.26.

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