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A frog needs two jumps in a row to leave a hole. The first succeeds 20% of the time, the second 30%, and any failure sends it back to the start. Find the expected number of jumps.

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A frog needs two successive jumps to leave a hole. The first jump succeeds with probability 20%, the second with 30%. If either jump fails it falls back and must start again from the first jump. What is the expected total number of jumps?

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