Suppose that 80 percent of all statisticians are shy, whereas only 15 percent of all economists are shy. Suppose also that 90 percent of the people at a large gathering are economists and the other 10 percent are statisticians. If you meet a shy person at random at the gathering. What is the probability that the person is a statistician?
+118609 This is how I tackled this problem.
I said let there be 1000 people present. It is easier to work with real numbers.
90 % are economists, which is 900 economists.
15% of those are shy, so that is 135 shy economists
10% of the 1000 people are statisticians so that is 100 statisticians.
80% of those are shy so that is 80 shy statisticians.
So there are 135+80=215 shy people at the gathering. And 80 of them are statisticians.
So that gives a probability of 80/215 = 16/43
