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13-Jun-2019 23:34

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Our task is to show that the best value of corresponds to 37% of .

We’ll do that by calculating the probability of landing X with your strategy, and then finding the value of that maximises this probability.

Before we start, here’s a picture of the end result.

It shows the values of on the horizontal axis and the best value of , the one that maximises the probability of ending up with X, on the vertical axis.

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Among your pool of people, there’s at least one you’d rate highest.In other words, you pick X if the highest-ranked among the first people turned up within the first people. In other words, you pick X if the highest-ranked among the first people turned up within the first people. If , so there are only five people, the only value of for which the two inequalities hold is , which is 40% of : So you should discard the first two people and then go for the next one that tops the previous ones.