It has been found that 70 of the art works in a certain gall

It has been found that 70% of the art works in a certain gallery are authentic (A) and the rest are fake (A\'). A collector decides if an art work is authentic or fake, and makes a mistake in 20% of his decisions. If the collector buys an art work thinking that it is authentic, find the probability that it is fake.

Solution

P ( Person thinking the painting is authentic)

= ( 0.70) (0.80) + (0.30)(0.20)

= 0.62

P ( Fake painting is thought of as authentic)

= (0.30) (0.20) / [( 0.70) (0.80) + (0.30)(0.20)]

= 0.0967

= 9.67%

Hope this helps.