SIG (Susquehanna)–styleTraderTraderQuestion #1
If you roll two dice and add their results, what is the probability of obtaining a sum of 6?
Free worked solution · Quant Blueprint
5/36, assuming two independent fair six-sided dice.
- Treat the dice as distinguishable: (1, 5) and (5, 1) are separate outcomes. There are 6 × 6 = 36 equally likely ordered pairs.
- The pairs summing to six are (1, 5), (2, 4), (3, 3), (4, 2) and (5, 1). That gives five favorable outcomes.
- Divide five by 36. A sum of seven has six favorable outcomes, which is a useful check that six should be slightly less likely.
Common mistake
Sums from two through twelve are not equally likely. Counting eleven possible sums and taking 1/11 gives the wrong sample space.
Follow-up
For a sum of at most six, the favorable counts are 1 + 2 + 3 + 4 + 5 = 15, giving 15/36 = 5/12.
Original educational explanation for this practice question. Reviewed . Firm-style practice; the label describes the collection’s preparation context.
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