at drataw 6 At the Dataw bank a vice president declared that

at drataw

6. At the Dataw bank a vice president declared that the proaty were being embezzled was .70 and that the probability that an embenemen wwsssw discovered by the bank examiner was 0.90, Given that the bank evamines dees se discovered by the bank examiner was 0.90. Given that ther bank examiner die, un embegzlement and that the examiner would not discover emberiemen sen ne ci embezzlement and that the examiner would not discover ember,etnern.wi thtens.onsd what is the probability that the bank\'s funds are not being embezned?

Solution

A:th banks funds are embezzeled

P(A)=0.7

B/A: the embezzelment is discovered, B: discovered

P(B/A)=0.9

we need to find P(A^C/B^C)

we use bayes theorem here

P(A^c/B^c)=P(B^c/A^c)*P(A^c)/P(A^c)=0.1*0.3/0.3=0.1