Conditional probability working backwards in a probability tree 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_ ? Thanks for your help!

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, $0.81\cdot0.72n=0.5832n$ like the new motorway **and** intend to drive more. You also know that $0.65n$ 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.)