At an art exhibition there are 12 paintings of which 10 are original. A visitor selects a painting at random and before decides to buy he asks the opinion of an expert about the authenticity of the painting. The expert is right in 9 out of 10 cases on average. Given that the expert decides the painting is authentic what is the probability it really is? If the expert decides the paining is a copy then the visitor returns it and chooses another one what is the probability that her second choice is an original?

a) 0.8333

b) 0.75

c) 0.8181 or 0.9090

Step-by-step explanation:

a)

The probability the visitor selects an authentic painting is

10/12 = 0.8333

b)

Since the opinion of the expert does not depend on your choice, the events are independent, so the probability that the expert says is authentic and it really is, is

0.8333*0.9 = 0.75

c)

If the expert decides the painting is a copy and it is not, then there are 11 paintings of which 9 are authentic, so the probability the visitor selects a new original painting is

9/11 = 0.8181

If the expert decides the painting is a copy and it is, then there are 11 paintings of which 10 are authentic, so the probability the visitor selects a new original painting is

10/11 = 0.9090