FRM Part I · FRM Exam Part I · Fundamentals of Probability
For a bond portfolio, let A = 'a fund's monthly return is negative' and B = 'the fund's monthly return exceeds 2%.' P(A) = 0.35 and P(B) = 0.25. Which statement is correct?
The events are mutually exclusive: a return cannot be both negative and above 2%. So the joint probability is zero and the union probability is 0.35 plus 0.25, or 0.60. They are neither independent nor exhaustive, since the union is below 1.
- AA and B are mutually exclusive, so P(A and B) = 0 and P(A or B) = 0.60Correct
- BA and B are independent, so P(A and B) = 0.0875
- CA and B are exhaustive, so P(A or B) = 1
- DA and B are mutually exclusive and exhaustive, so P(B) must equal 0.65
Explanation
A return cannot be both negative and above 2%, so the events are mutually exclusive and P(A or B) = 0.35 + 0.25 = 0.60. They are not independent, since knowing A occurred makes B impossible (P(B|A) = 0 differs from 0.25). They are not exhaustive because 0.60 is below 1; returns between 0% and 2% belong to neither.
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?
- For two events X and Y, P(X) = 0.30, P(Y) = 0.50 and P(X and Y) = 0.12. 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 …