Question

Suppose that 70% of the statisticians are shy, whereas 30% of the economist are shy. Suppose also that 80% of the people at a large gathering are economists and the remaining 20% are statisticians. If you randomly meet a person at the gathering and the person is shy, what is the probability that the person is a statistician?

Answer 1

Answer:

The probability that a randomly selected person who is shy is a Statistician is 0.3684.

Step-by-step 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:

$P(X) = P(X|S)P(S)+P(X|E)P(E)\\=(0.70\times0.20)+(0.30\times0.80)\\=0.38$

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:

$P(A|B)=\frac{P(B|A)P(A)}{P(B)}$

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

$P(S|X)=\frac{P(X|S)P(S)}{P(X)}=\frac{0.70\times0.20}{0.38}= 0.3684$

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