Beyond Common Core
Problem 29 of 45s12-029
Each spin of a spinner lands on green with probability , independently. What is the probability the first green is on the 3rd spin, and the mean number of spins until the first green?
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Solution walkthrough1:36
- Geometric: spin until the first green. Each spin is independent with .
- First green on spin means exactly this: miss, miss, then green.
- Multiply: . In general .
- Mean of a geometric count: spins, counting the green one.
- Traps: lets the green be anywhere, swaps the chances, and mean counts only misses.