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pudro November 10th, 2008 08:12 PM

Stats question: The Secretary Question word problem
 
Suppose you will meet 4 people who you might consider marrying. Or suppose you will interview 4 job applicants. In either case, you will meet them only one at a time and if you don't select a person, you can not go back to that person later. Only after you see them all, you would then be able to rank which was the best. However, as you see one after another, you can rank each based on those you have seen so far.

1. Suppose you use the selection procedure that you will pass over the first person and select the first person you meet who is better than the one passed. What is the probability this procedure will lead to selecting the best of the 4 people? Write your answer as a reduced fraction.

2. Suppose you use the selection procedure that you will pass over the first two people you see and select the best person you see after that? Write your answer as a reduced fraction.

Now, suppose the number of people you will meet is increased to 10.

3. If you let the first 3 pass and select the first person better than any of the preceding, what is the probability this will lead to selecting the best person in the whole group? Round answer to 4 places after the decimal.

4. If you let the first 5 pass and select the first person better than any of the preceding, what is the probability this will lead to the selection of the best person in the group? Round answer to 4 places after the decimal.

5. Give a decimal approximation for the number e. Round answer to 4 places after the decimal.

6. Suppose you will interview 20 job applicants and once turned down, you would not be able to return to an applicant. How many should you pass over before selecting the next applicant better than all of those that preceded? Write the exact answer as a ratio. Round off the answer to the nearest integer .


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