40 0 20 dating show
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.
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.