2014 UNCO Math Contest II Problems/Problem 8
In the Queen’s croquet, a game begins with the ball at the bottom wicket. All players hit the same ball. Each player hits the ball from the place the previous player has left it. When the ball is hit from the bottom wicket, it has a % chance of going to the top wicket and a % chance of staying at the bottom wicket. When hit from the top wicket, it has a % chance of hitting the goal post and a 50% chance of returning to the bottom wicket.
(a) If Alice makes the first hit and alternates hits with the Queen, what is the probability that Alice is the first player to hit the goal post with the ball?
(b) Suppose Alice, the King, and the Queen take turns hitting the ball, with Alice playing first. Now what is the probability that Alice is the first player to hit the goal post with the ball?
|2014 UNCO Math Contest II (Problems • Answer Key • Resources)|
|1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10|
|All UNCO Math Contest Problems and Solutions|