SOLUTION: Where people turn to for news is different for various age groups.Suppose that a study conducted on this issue was based on 200 espondents who were between the ages of 36 and 50, a

Question 1142444: Where people turn to for news is different for various age groups.Suppose that a study conducted on this issue was based on 200 espondents who were between the ages of 36 and 50, and 200 respondents who were over age 50. Of the 200 respondents who were between the ages of 36 and 50, 82 got their news primarily from newspapers. Of the 200 respondents who were over age 50, 104 got their news primarily from newspapers
If a respondent is selected at random, what is the probability that he or she
(a) got news primarily from newspapers?
(b) got news primarily from newspapers and is over 50 years old?
(c) got news primarily from newspapers or is over 50 years old?
(d) Explain the difference in the results in (b) and (c).
(e) Suppose that two respondents are selected. What is the probability that both got news primarily from newspapers?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
200 out of 400 are between 36 and 50
200 out of 400 are over 50
82 out of the 200 who are between 36 and 50 get their news primarily from newspapers.
104 out of the 200 who are over 50 get their news primarily from newspapers.

If a respondent is selected at random, what is the probability that he or she

(a) got news primarily from newspapers?

that would be (82 + 104) / 400 = 186 / 400 = .465

(b) got news primarily from newspapers and is over 50 years old?

that would be 104 / 400 = .26

(c) got news primarily from newspapers or is over 50 years old?

that would be 186 / 400 + 200 / 400 - 104 / 400 = 282 / 400 = .705

the reason for the subtraction is that 104 people are includes in both the people that get their new primarily from newspapers and also includes in the people that are over 50.
because of that, 104 are being double counted which requires 104 to be subtracted so that the double counting is removed.

(d) Explain the difference in the results in (b) and (c).

in (b), the person has to be over 50 and get their news primarily from the newspaper. that's a select group that only includes people over 50.

in (c), the person has to get their news primarily from newspapers or be over 50.
that includes people under 50 who get their news primarily from newspapers and also includes people over 50 who do not get their news primrily from newspapers.

(e) Suppose that two respondents are selected. What is the probability that both got news primarily from newspapers?

the probability that the first person picked got their news primarily from newspapers is 186 / 400.

assuming that person got their news primarily from newspapers, the probability that the second person picked got their news primarily from newspapers is now 185 / 399.

the probability that both got their news primarily from newspapers is therefore 186 / 400 * 185 / 399.

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