"I currently have this question.. A survey was conducted that found 72% of respondents liked the new motorway. Of all respondents, 65% intend to drive more. Suppose that 81% of those who like the new motorway intend to drive more. I get rather confused with how the 65% and 81% intertwine. I assume I'm working backwards to find out the percentage of those who don't like the new motorway but intend to drive more. Let l = like, d = drive.. pr(l) = 0.72 , pr(l') = 0.28 Would I be right in claiming that pr(d) = 0.65 therefore pr(d | l) = 0.65/0.72 ?"

madeeha1d8 2022-09-17 Answered
I currently have this question..
A survey was conducted that found 72% of respondents liked the new motorway. Of all respondents, 65% intend to drive more. Suppose that 81% of those who like the new motorway intend to drive more.
I get rather confused with how the 65% and 81% intertwine. I assume I'm working backwards to find out the percentage of those who don't like the new motorway but intend to drive more.
Let l = like, d = drive..
pr(l) = 0.72, pr(l') = 0.28
Would I be right in claiming that pr(d) = 0.65 therefore pr(d/l) = 0.65/0.72 ?
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Answers (1)

seguidora1e
Answered 2022-09-18 Author has 4 answers
HINT: Let n be the number of respondents. You know that 0.72n like the new motorway, and that 81% of those 0.72n intend to drive more.
Thus, 0.81 0.72 n = 0.5832 n like the new motorway and intend to drive more. You also know that 0.65 n intend to drive more. Thus, the number who intend to drive more but do not like the new motorway must be ... ? (Of course once you have the number, you can express it as a percentage easily enough.)
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