Question

S. (4) A credit union is accounts card ac o within/ proba sues two types of credit cards, Platinum and Gold. The Platinum card for 25% of the cards i unts go delinquent within the first year, while 3% of Gold card accounts go delinquent first year. If 2.5% of all accounts go delinquent within the first year, then find the ssued, and the Gold card accounts for the rest. 1% of platinum that a random delinquent account is from a Gold card.

Answer 1

Let P denote a Platinum card
Let G denote a Gold card
Let D denote a delinquent account

Probability of Platinum card = P(P)=0.25
Probability of Gold card = P(G)=0.75
Probability an account is delinquent given it platinum card = P(D|P)= 0.01
Probability an account is delinquent given it gold card = P(D|G)= 0.03

Probability an account is delinquent = P(D)= 0.025

We need to find probability of gold card given that is delinquent account

PlG|D) = P(DIG) x P(G) 0.03 × 0.75 0.025 0.9 P D