Questions / Quant trading, Counting & stopping
Two dice, then a condition
Two fair six-sided dice are rolled independently. How many of the 36 ordered outcomes sum to 8?
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Answer: 5 outcomes
- The 36 outcomes are ordered pairs: the first coordinate identifies the first die.
- For a sum of eight, valid pairs are (2,6), (3,5), (4,4), (5,3), and (6,2).
- There are five pairs. The pair (1,7) is impossible; (2,6) and (6,2) are separate outcomes.
Interview shortcut. For two dice, a sum s has 6 − |s − 7| ordered ways: 8 has 5.
Takeaway. Keep the event count and sample-space convention consistent.
In the app this has a follow-up where one thing about the setup changes. Try the follow-up.