Question: (Tom Sawyer Problem) You are given a task, say painting a fence. The probability that the task will be completed if k friends are helping

(Tom Sawyer Problem) You are given a task, say painting a fence. The probability that the task will be completed if k friends are helping you is pk (k = 0, 1, ...). If j friends already helped you, the probability that the (j + 1)st will also help is πj (j =

0, 1, ...). On the other hand, if the jth friend did not help, then the (j + 1)st will not help either. (i) Find the probability that the task will be completed. (ii) Solve part (i) if pk = 1 − λk,πj = μ for all j.

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