Question

In a bank vault, 0.5% of the bills are fake. One of the cashiers is very good in spotting fake bills, and given that the bill is fake, he correctly classifies it as such 99% of the time. However, 2% of the real bills he examines are misclassified as being fake. For a random bill taken from the vault,

i. what is the probability that the cashier will claim it is fake?

ii. what is the probability that the bill is in fact fake, given that the cashier identified it as such?

Answer 1

i)

P(cashier will claim bill is fake)=P(bill is fake)*P(cashier will claim bill is fake|bill is fake)+P(bill is not fake)*P(cashier will claim bill is fake|bill is not fake)

=0.005*0.99+(1-0.005)*0.02=0.02485

ii)

P(bill is fake| cashier will claim bill is fake)

=P(bill is fake)*P(cashier will claim bill is fake|bill is fake)/P(cashier will claim bill is fake)

=0.005*0.99/0.02485=0.1992