Question

2 (10 points). A credit card company divides its customers into two categories: low risk and high risk, based on a certain credit score. According to company's satistics, 10% of customers are high risk and the rest are low risk. The chances that a low risk customer will miss a payment or not pay his/her full balance on time at least once in any given year are 5%, while these chances increase to 30% for high risk customiers. If a custonner missed a payment in the last year, what are the chances that he/she will miss a payment or will not pay a balance in full in the coming year? Hint: Use conditional independence.

Answer 1

Let P(x) denote the probability of an event x.
So, P(L) and P(H) denote the probabilities that the customer is low risk and high risk respectively.
According to the given question,
P(H)=0.1

P(L)=1-0.1=0.9

Let M denote the event that a customer missed a payment.
Therefore,
P(M/L) denotes the probability that a low risk customer missed a payment and P(M/H) denotes the probability that a high risk customer missed a payment.
So, P(M/L)=0.05 and P(M/H)=0.3.
We need to find P(M).
Using the formula for total probability, we get
$P(M)=P(M/L)*P(L)+P(M/H)*P(H)$

we get P(M)=0.075 or 7.5%.
Ans=7.5%