Question: 4.3.5 (Tom Sawyer Problem) You are given a task, say painting a fence. The probability that the task will be completed if k friends are

4.3.5 (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 7-rj (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 p k = 1 - A k , 7-rj = p for all j .

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