FRM Part I · FRM Exam Part I · Fundamentals of Probability
A trader has two independent strategies. Strategy X profits on a given day with probability 0.60 and strategy Y with probability 0.50. Given that exactly one strategy profits on a day, what is the probability that it is strategy X?
The probability is 0.60. X profits alone with probability 0.30 and Y profits alone with probability 0.20, so exactly one profits with probability 0.50. Dividing 0.30 by 0.50 gives 0.60, matching option 0.600 rather than 0.545 or 0.300.
- A0.600
- B0.500
- C0.545Correct
- D0.300
Explanation
P(X only) = 0.60 x 0.50 = 0.30. P(Y only) = 0.40 x 0.50 = 0.20. P(exactly one) = 0.50. P(X | exactly one) = 0.30/0.50 = 0.60. So the correct value is 0.600.
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