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?

37.21% probability that the person is a statistician.

Step-by-step explanation:

We have these following probabilities:

An 80% probability that a statistican is shy.

A 15% probability that an economist is shy.

At the gathering, a 90% probability that a person is an economist.

At the gathering, a 10% probability that a person is a statistican.

If you meet a shy person at random at the gathering. What is the probability that the person is a statistician?

This can be formulated as the following question:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

So

What is the probability that the person is a statistican, given that he is shy?

P(B) is the probability of the person being a statistican. So P(B) = 0.1.

P(A/B) is the probability of a statistican being shy, so P(A/B) = 0.8.

P(A) is the probability of a person being a shy. This is 15% of 90%(economists) and 80% of 10%(statisticans). So

Finally

37.21% probability that the person is a statistician.

answer: a) 56% women

b)44% men

step-by-step explanation:

the answer to your question is b.