2019 AIME II Problems/Problem 2
Problem 2
Lily pads lie in a row on a pond. A frog makes a sequence of jumps starting on pad . From any pad the frog jumps to either pad or pad chosen randomly with probability and independently of other jumps. The probability that the frog visits pad is , where and are relatively prime positive integers. Find .
Solution
Let be the probability the frog reaches pad starting from pad . Then , , and for all integers . Working our way down to , we find . .
See Also
2019 AIME II (Problems • Answer Key • Resources) | ||
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