In rural Ireland, a century ago, the students had to form aline. The student at

Question

In rural Ireland, a century ago, the students had to form aline. The student at the front of the line would be asked tospell a word. If he spelled it correctly, he was allowed tosit down.   If not, he received a whack on the hand witha switch and was sent to the end of the line. Suppose thatthe student could spell correctly 70% of the words in alesson. What is the probability that the student would beable to sit down before receiving four whacks on the hand? Assumethat the master chose the words to be spelled randomly andindependently.

Explanation / Answer

Note: P(receiving 4 whacks in a row) = P(receiving 1 whack)^4because the trials are independent. Thus, P(not receiving 4 whacks in a row) = 1 - P(receiving 4 whacksin a row) = 1 - P(receiving 1 whack)^4 1 - (1-.7)^4 .9919

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