A survey showed that 23 % 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.
To solve this problem, we can use conditional probability.
(a) To find the probability that a student watches TV news regularly given that they read newspapers regularly, we need to use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
Given that 21% of college students both follow TV news regularly and read newspapers regularly, and that 23% of college students read newspapers regularly, we have the following values:
P(A and B) = 21% = 0.21
P(B) = 23% = 0.23
Plugging these values into the formula, we get:
P(A|B) = 0.21 / 0.23 = 0.913
So, the probability that a student watches TV news regularly, given that they regularly read newspapers, is approximately 0.91 (rounded to 2 decimal places).
(b) To find the probability that a randomly selected college student reads newspapers regularly, given that they watch TV news regularly, we can use the same formula:
P(B|A) = P(A and B) / P(A)
Given that 21% of college students both follow TV news regularly and read newspapers regularly, and that 82% of college students regularly watch the news on TV, we have the following values:
P(A and B) = 21% = 0.21
P(A) = 82% = 0.82
Plugging these values into the formula, we get:
P(B|A) = 0.21 / 0.82 = 0.26
So, the probability that a randomly selected college student reads newspapers regularly, given that they watch TV news regularly, is approximately 0.26 (rounded to 2 decimal places).