CA Foundation · Quantitative Aptitude · Probability
In a Mumbai firm, 70% of employees are graduates. Of the graduates, 40% are in the finance team, and of the non-graduates, 10% are in the finance team. An employee chosen at random is found to be in the finance team. What is the probability that the employee is a graduate?
The probability is 28/31. The finance team share from graduates is 0.7×0.4 = 0.28 and from non-graduates 0.3×0.1 = 0.03, total 0.31. Dividing the graduate part by the total gives 0.28/0.31 = 28/31.
- A28/31Correct
- B28/100
- C7/10
- D21/31
Explanation
P(G and F) = 0.7 × 0.4 = 0.28. P(NG and F) = 0.3 × 0.1 = 0.03. P(F) = 0.31. By Bayes' theorem P(G|F) = 0.28/0.31 = 28/31. The option 28/100 is the joint probability, not the conditional one.
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