CA Foundation · Quantitative Aptitude · Probability
In a financial institution, the probability that a loan application is approved by the manager is 0.7. If the application is approved by the manager, the probability that it passes the final audit is 0.9. However, if the application is not approved by the manager, it is rejected before reaching the audit. What is the probability that a randomly selected application is both approved by the manager and passes the final audit?
Since passing the audit is conditional on manager approval, we use the multiplication rule: P(both events) = 0.7 × 0.9 = 0.63.
- A0.70
- B0.63Correct
- C0.90
- D0.60
Explanation
This is a conditional probability problem using the multiplication rule. P(approved and passes audit) = P(approved by manager) × P(passes audit | approved by manager) = 0.7 × 0.9 = 0.63. The distractor 0.70 represents only manager approval, 0.90 represents only audit pass rate, and 0.60 results from subtracting instead of multiplying.
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