Answer:
The probability that a randomly selected person who is shy is a Statistician is 0.3684.
Explanation:
Let's denote the events as follows:
E = a person is an Economist
S = a person is a Statistician
X = a person is shy.
Given:
P (E) = 0.80
P (S) = 0.20
P (X|S) = 0.70
P (X|E) = 0.30
Compute the probability that a randomly selected person is shy is:

The probability that a person is shy is, P (X) = 0.38.
The conditional probability of an event A provided that another event B has already occurred is:

Compute the probability that a randomly selected person who is shy is a Statistician as follows:

Thus, the probability that a randomly selected person who is shy is a Statistician is 0.3684.