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.

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

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    2021-11-10T16:26:49+00:00

    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 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:

    A = a + (A \cap B)

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

    By the same logic, we have that:

    B = b + (A \cap B)

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

    This means that A \cap B = 0.21

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

    This means that A = 0.24.

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

    This means that B = 0.82

    (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.

    P(B|A) = \frac{A \cap B}{A}

    So

    P(B|A) = \frac{0.21}{0.24} = 0.88

    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.

    P(A|B) = \frac{A \cap B}{B}

    So

    P(A|B) = \frac{0.21}{0.82} = 0.26

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

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