Question

A survey asked people of different ages whether they get their news by

reading the paper. What is the probability that a person surveyed is under 40,
given that he or she gets the news by reading the paper? If necessary, round
Don't read
Read paper
Total
paper
36
your answer to the nearest percent.
Under 40
40 or older
Total
4
24
28
16
52
40
40
80

Answer 1

To find the probability that a person surveyed is under 40 given that he or she gets the news by reading the paper, we need to use Bayes' theorem:

P(Under 40 | Read paper) = P(Read paper | Under 40) * P(Under 40) / P(Read paper)

where

P(Under 40 | Read paper) is the probability that a person is under 40 given that he or she gets the news by reading the paper

P(Read paper | Under 40) is the probability that a person under 40 reads the paper (36/80)

P(Under 40) is the overall probability of selecting a person under 40 (40/80)

P(Read paper) is the overall probability of selecting a person who reads the paper, calculated as the sum of those who are under 40 and read the paper and those who are 40 or older and read the paper (36+24)/(80)

Plugging in the values, we get:

P(Under 40 | Read paper) = (36/80) * (40/80) / ((36+24)/80)

P(Under 40 | Read paper) = 0.6

So the probability that a person surveyed is under 40, given that he or she gets the news by reading the paper, is 60%.