Question

1 A stockbroker predicts whether a stock will go up or down by tossing a coin and so has a 50% chance of making a correct prediction. Another broker, who is skilled, has a 60% chance of making a correct prediction. You don’t know which broker is which, so you watch their predictions for three days. Each broker gets all three predictions correct. What are the relevant probabilities? How do you decide who is the skilled broker?

2. A statistician went deer hunting. He saw a deer. His first shot was 10 inches to the left of the deer. He shot again. His second shot was 10 inches to the right of the deer, upon which the statistician exclaimed, “I got him!” What did he mean by that?

Answer 1

Question. no. 2

When the statistician exclaimed that "I got him!" after the second shot he meant that he on average hit the deer since the first time his shot was 10 inches to the left of the deer and the second shot was 10 inches to the right of the deer, he wrongly concludes that he on average hit the deer.

This example is used by statisticians and teachers of statistics and related fields to illustrate the fact that calculating the mean/average is not the solution in every case and that other sample statistics might also be relevant for the study and should be considered.

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Mohit