Subscribers to a local newspaper were asked whether they regularly, occasionally
ID: 3177200 • Letter: S
Question
Subscribers to a local newspaper were asked whether they regularly, occasionally, or never read the business section and also whether they had traded last common stocks (or shares in a mutual fund) over the last year. the table shown here indicates the proportions of subscribers in six joint classifications. What is the probability that a randomly chosen subscriber never reads the business section? What is the probability that a randomly chosen subscriber has traded stocks over the last year? What is the probability that a subscriber who never reads the business section has traded stocks over the last year? What is the probability that a subscriber who traded stocks over the last year never reads the business section? What is the probability that a subscriber who does not regularly read the business section traded stocks over the last year?Explanation / Answer
Solution:-
a) The probability that a randomly chosen subscriber never reads the bussiness section is 0.25.
Probability that a randomly chosen subscriber never reads the bussiness section = 0.21 + 0.04
The probability that a randomly chosen subscriber never reads the bussiness section = 0.25.
b) The probability that a randomly chosen subscriber has traded stocks over the last year is 0.32
The probability that a randomly chosen subscriber has traded stocks over the last year = 0.18 + 0.10 + 0.04
The probability that a randomly chosen subscriber has traded stocks over the last year = 0.32
c) The probability that a randomly chosen subscriber never reads the bussiness section has traded stocks over last year is 0.16.
The probability that a randomly chosen subscriber never reads the bussiness section = 0.25
The probability that a randomly chosen subscriber has traded stocks over last year and never reads bussiness section = 0.04
The probability that a randomly chosen subscriber never reads the bussiness section has traded stocks over last year = 0.04/0.25 = 0.16
d) The probability that a subsciber who traded stocks over the last year never reads the bussiness sections is 0.125.
The probability that a randomly chosen subscriber has traded stocks over last year and never reads bussiness section = 0.04
The probability that a randomly chosen subscriber has traded stocks over the last year = 0.32
The probability that a subsciber who traded stocks over the last year never reads the bussiness sections = 0.04/0.32 = 0.125