CA Foundation · Quantitative Aptitude · Probability
A bank in Chennai finds that 20% of its loan customers are defaulters. Past records show that 80% of defaulters had a poor credit score, while only 10% of non-defaulters had a poor credit score. A customer with a poor credit score applies. What is the probability the customer is a defaulter?
The probability is 2/3. Defaulters with poor scores are 0.2×0.8 = 0.16 of all customers, non-defaulters with poor scores are 0.8×0.1 = 0.08, so the total is 0.24. Dividing 0.16 by 0.24 gives 2/3.
- A1/2
- B4/5
- C2/3Correct
- D16/25
Explanation
P(default and poor) = 0.2 × 0.8 = 0.16. P(non-default and poor) = 0.8 × 0.1 = 0.08. Total = 0.24. Posterior = 0.16/0.24 = 2/3. The option 4/5 is only P(poor | default), the wrong conditional.
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