Difference between revisions of "2022 AMC 8 Problems/Problem 25"
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Revision as of 16:31, 28 January 2022
Problem
A cricket randomly hops between leaves, on each turn hopping to one of the other
leaves with equal probability. After
hops what is the probability that the cricket has returned to the leaf where it started?
Solution
Denote to be the probability that the cricket would return back to the first point after
Hops. Then, we get the recursive formula
because if the leaf is not on the target leaf, then there is a
probability that he’ll make it back. With this formula and the fact that
we have:
so our answer is
~wamofan
See Also
2022 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Last Problem | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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