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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?

 Feb 13, 2020
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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

 Feb 13, 2020

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