CMA Foundation · Fundamentals of Business Mathematics and Statistics · Probability
In a bank branch in Jaipur, 70% of loan applicants are salaried and 30% are self-employed. The probability of default is 2% for salaried and 8% for self-employed borrowers. A loan is found to have defaulted. What is the probability that the borrower was self-employed?
The probability is about 0.63. Total default probability is 0.038, of which the self-employed contribute 0.024, so the posterior is 0.024 divided by 0.038, which is roughly 0.63.
- A0.30
- B0.60Correct
- C0.63
- D0.24
Explanation
P(default) = 0.7×0.02 + 0.3×0.08 = 0.014 + 0.024 = 0.038. P(self-employed | default) = 0.024/0.038 = 12/19 ≈ 0.63. So the correct option is 0.63, and 0.24 is a wrong choice that uses the joint figure scaled incorrectly.
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