1) A top NHL hockey player scores on 93% of his shots in a shooting competition. What is the probability that the player will not miss the goal until his 20th try?
Discuss whether this problem is describing a binomial distribution or a geometric distribution. What event is considered a success? What event is considered a failure? Explain your answers to both and solve the problem.
2) Describe a scenario where you believe a binomial distribution would be appropriate. Describe a scenario where you believe a geometric distribution would be appropriate. Explain your reasoning for both scenarios. Discuss what could have gone wrong (from a probability standpoint) with this type of game-fixing. How confident should the conspirators have been that this plan would work? Does the selection of any of the numbers affect the selection chances of the other two numbers, and explain your reasoning.