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FRM Part I · FRM Exam Part I · Fundamentals of Probability

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?

X and Y are negatively dependent. The conditional probability P(X given Y) is 0.12 divided by 0.50, or 0.24, which is lower than the unconditional 0.30. Independence would require a joint probability of 0.15, not 0.12.

  1. AX and Y are independent because P(X and Y) is positive
  2. BX and Y are mutually exclusive because P(X) + P(Y) < 1
  3. CX and Y are positively dependent because P(X | Y) = 0.24 is below P(X)
  4. DX and Y are negatively dependent because P(X | Y) = 0.24 is below P(X)Correct

Explanation

P(X | Y) = 0.12 / 0.50 = 0.24, which is below P(X) = 0.30. Independence would need a joint probability of 0.15, so the events are not independent. Learning Y occurred lowers the probability of X, so the dependence is negative. They are not mutually exclusive since the joint probability is positive.

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