Among all Californians there are 0 01 people who received b

Among all Californians, there are 0 : 01% people who received bribes. The CIA devised a special test such that if applied to an innocent person, it gives PLUS with probability 90%, and MINUS with probability 10%. If applied to a criminal, it gives PLUS with probability 10%, and MINUS with probability 90%. It is applied to a random person three times. On the 1st two tries, it gave MINUS; for the third time, it gave PLUS. What is the probability that this is a criminal?

Solution

. What is the probability that this is a criminal?

P = 0.90*0.90 * 0.10 = 0.081