1. The problem statement, all variables and given/known data Although Robin Hood gets a bullseye with probability 0.9, he finds himself facing stiff competition in the tournament. To win he must get at least four bullseyes with his next five arrows. However, if he gets five bullseyes, he risks exposing his identity to the sheriff. Assume that if he wishes to, he can miss the bullseye with probability 1. What is the probability that Robin wins the tournament without risking exposing his identity? 2. Relevant equations 3. The attempt at a solution From the problem description, it seems like Robin is free to miss any one of the next five shots. However, I assumed that he would try to hit the first four and purposefully miss the last (I'm not sure if this assumption is valid or if I need to consider other cases). The chance of Robin hitting the first four and missing the last one is exactly 0.9 * 0.9 * 0.9 * 0.9. However, Robin could also accidentally miss one of the first four, which would force him to hit the rest. The probability that Robin misses a shot and hits the rest is 0.1 * 0.9 * 0.9 * 0.9 * 0.9. There are exactly 4 ways that this situation could occur (i.e., Robin misses the first shot, Robin misses the second shot, etc), so the total probability would be 4 * 0.1 * 0.9 * 0.9 * 0.9. Then, we can sum up the above two probabilities (they're disjoint since either Robin makes the first four or he doesn't).