Question

A bank classifies its customer into two classes "fraud" and "normal" based on their installment payment behavior. We know that the probability of a customer being fraud is P(fraud)=0.20, the probability of customer defaulting installment payment is p(default)=0.40,and the probability that a fraud customer defaults in installment payment is p(default|fraud)=0.80. What is the probability of a customer who defaults in payment being a fraud?A.0.80 B.0.60 C.0.40 D.0.20

Answer 1

The probability of a customer who defaults in payment being a fraud is 0.40

Given the,

• probability of a customer being fraud  =is
• P(fraud)=0.20

• the probability of customer defaulting installment payment is
• p(default)=0.40
• the probability that a fraud customer defaults in installment payment is
• p(default/fraud)=0.80 = p(default ∧ fraud)/p(fraud)

We need to find the probability of a customer who defaults in payment being a fraud.

• This is P(fraud/ default ) = p( fraud ∧ default)/p (default)

Multiplying and dividing by P(fraud)

• P(fraud/ default ) =    p( fraud ∧ default)/p(default)x $\frac{p(fraud)}{p(fraud)}$

• P(fraud/ default ) = p( fraud ∧ default) / p(fraud) x p(fraud)/p(default)

• P(fraud/ default )  = 0.80 x 0.20/0.40 = 0.40