Citadel–styleAnalystQuantitative AnalystQuestion #67
Suppose you roll two fair six-sided dice. What is the probability that the sum of the two dice is equal to 8?
Free worked solution · Quant Blueprint
5/36.
- Label the dice A and B so that outcomes are ordered. Independence and fairness make all 36 pairs equally likely.
- The five pairs are (2,6), (3,5), (4,4), (5,3) and (6,2).
- Divide the favorable count by 36. Reflection x → 7 − x maps sum eight to sum six, so those sums must have equal probabilities.
Common mistake
Counting (2,6) and (6,2) as one outcome loses a distinct equally likely pair.
Follow-up
For a target sum s between 2 and 12, the count is 6 − |7 − s|, giving probability (6 − |7 − s|)/36.
Original educational explanation for this practice question. Reviewed . Firm-style practice; the label describes the collection’s preparation context.
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