James makes 20% of his hook shots. Kristy makes 30% of hers. Hannah makes 40% of hers. They play this game: the players take turns shooting and the first player to make the shot wins. Then they start over and play again, and again, and so on.
If the order of shooting is James, then Kristy, then Hannah, which of the following statements are true:
Kristy wins most often.
Because Hannah is best at this shot, she is more likely to win than Kristy.
James will win least often.
James, Kristy and Hannah all win the same number of games.
James will win at least as often as either of the others.
Solution
In the first round, James shoots first and wins: 20% of the time. Kristy gets a chance next, in 80% of the games, and wins 30% of those, for a total of 24% – on the first round. Finally Hannah gets to shoot in only 56% of the first round games and will win 40% of these for a total of 22.4% – so far.
Subsequent rounds of course simply repeat these percentages. On the basis of only the first round we can make comparisons. So, a is true, b is false, c is true, d is false and e is false.
The only true statements are a and c.