
Explanation:
We use Bayes' theorem to find the probability that a candidate comes from India given that they passed the exam.
Let be the total probability of a candidate passing the exam, which is calculated using the law of total probability:
Now, we find the conditional probability of the candidate being from India given they passed:
The probability is closest to 24%.
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Q.25 The FRM part 1 exam attracts candidates from all over the world. A quantitative analyst compiled the following statistics:
| Country of residency | Probability of passing the FRM Part 1 exam | A portion of total candidates |
|---|---|---|
| United States | 0.40 | 0.22 |
| India | 0.42 | 0.21 |
| Canada | 0.39 | 0.14 |
| Other | 0.31 | 0.44 |
If a randomly selected candidate has just passed the FRM part 1 exam, the probability that the candidate comes from India is closest to:
A
22%
B
24%
C
25%
D
9%