FRM Part I · FRM Exam Part I · Fundamentals of Probability
Which statement about Bayes' theorem is correct?
Bayes' theorem says P(A|B) equals P(B|A) times P(A) divided by P(B). It reverses the conditioning using the prior and the total probability of the evidence. A high likelihood does not guarantee a high posterior when the prior is small.
- AP(A|B) always equals P(B|A) when A and B are dependent.
- BThe posterior probability of A given B equals P(B|A) x P(A) divided by P(B).Correct
- CThe posterior probability of A given B equals P(B|A) divided by P(A) x P(B).
- DIf P(B|A) is high, P(A|B) must also be high regardless of the prior P(A).
Explanation
Bayes' theorem states P(A|B) = P(B|A)P(A)/P(B). The conditional probabilities are generally not equal, and a low prior P(A) can make the posterior low even when P(B|A) is high (base rate effect).
Did you get it right without looking?
One question tells you little. A timed set on Fundamentals of Probability shows your real accuracy, how long you take and where you lose marks.
More Fundamentals of Probability questions
- Random variables X and Y have Var(X) = 25, Var(Y) = 16 and Cov(X,Y) = 10. What is the correlation between (X + Y) and (X - Y), to two decima…
- A bank's fraud model flags 5% of all transactions. Of flagged transactions, 40% are actually fraudulent. Of unflagged transactions, 1% are f…
- Which statement about events A and B, each with positive probability, is correct?
- X is equally likely to be -1, 0 or +1, and Y = X². Which statement is correct?
- An insurer finds that 60% of policyholders are urban and 40% rural. The probability of a claim in a year is 10% for urban and 25% for rural …
- In a loan portfolio, 5% of borrowers default within a year. Of the defaulting borrowers, 80% had been flagged by an early-warning model. Of …