What to know
Identify the rule, formula, or decision criterion before reading the answer choices. CFA Level I distractors often use the right vocabulary with the wrong condition.
Quantitative Methods
Probability Trees and Conditional Expectations practice questions
Probability Trees and Conditional Expectations is part of CFA Level I Quantitative Methods. Quantitative Methods questions emphasize time value of money, probability, sampling, hypothesis testing, regression, and return statistics. Use this page to review the controlling ideas, then work through 8 questions with answer explanations and common traps.
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Work each item under time pressure, then compare your reasoning with the step-by-step explanation and key takeaway.
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Missed questions should become scheduled reviews when the error comes from a concept gap, formula setup, or answer-choice trap.
Quantitative Methods
Probability Trees and Conditional Expectations
An asset has returns of -10%, 5%, and 15% with probabilities 20%, 50%, and 30%. The expected return is closest to:
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Probability Trees and Conditional Expectations
If P(A and B) = 0.18 and P(B) = 0.30, P(A | B) is closest to:
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Probability Trees and Conditional Expectations
A model assigns a 60% probability to expansion. If expansion occurs, the probability of a positive earnings surprise is 80%; if recession occurs, it is 30%. The unconditional probability of a positive surprise is closest to:
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Probability Trees and Conditional Expectations
If the economy expands, a stock is expected to return 12%; if it contracts, it is expected to return -6%. Given a 70% probability of expansion, the expected return is closest to:
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Probability Trees and Conditional Expectations
For returns of -10%, 5%, and 15% with probabilities 20%, 50%, and 30%, the standard deviation is closest to:
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Probability Trees and Conditional Expectations
Thirty percent of analysts are skilled. A favorable signal occurs 80% of the time for a skilled analyst and 25% of the time for an unskilled analyst. Given a favorable signal, the probability the analyst is skilled is closest to:
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Probability Trees and Conditional Expectations
A strategy loses 4 if a signal is wrong and gains 6 if the signal is correct. The signal is correct with probability 65%. The expected payoff is closest to:
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Probability Trees and Conditional Expectations
A risk report gives P(Default | Downgrade) = 18% and P(Downgrade | Default) = 60%. The analyst uses 60% as the probability of default after a downgrade. The analyst most likely confused:
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