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?

Guest Feb 13, 2020

#2**+2 **

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

Melody Feb 13, 2020