Probability Recall that events are called independent if knowing the outcome of one event doesn't change the probability of another event. For example, when flipping a coin five times in a row, each flip is independent because it does not affect the next. When events are independent, we can multiply their individual probabilities together to find the probability that they all happen at once or in succession. For this activity, you may want to watch this video. https://www.youtube.com/watch?v=4IjRtsJ54Nw&t=14s 1. 2 pts: A free throw is a penalty shot in basketball. One of the NBA's best free throw shooters is Stephen Curry, making 90.6% of his free throws. Assume for a moment that free throws are independent events. What is the probability that Curry will make 6 free throws in a row? 2. 2 pts: Curry is fouled in many 3-point situations, so he often takes 3 free throws at a time. When he takes 3 free throws, what is the probability that he makes the first two but misses the last one? 3. 4 pts: Assume each of Curry's free throw attempts are independent. What is the probability that he makes at least one of his next 4 free throws? Show your work. 4. 3 pts: Are free throws actually independent events? Why or why not? 5. 2 pts: Kobe Bryant made 44.7% of the shots he took in his career. When a player starts to make many shots in a row, the "hot hand" theory says that their probability of making shots is higher than normal. Let's assume the "hot hand" doesn't exist. What is the probability that Kobe makes 8 shots in a row? 6. 2 pts: In his career, Kobe took 30,697 shots. Given this information and the probability of an 8-shot streak in Question 3, what is the expected number of times Kobe would get an 8-shot streak by chance? 7. 5 pts: Kobe's actual number of 8-shot streaks over his career was 47. Is this enough to prove or disprove the "hot hand" theory? If not, how else could you test the theory? Discuss. This assignment is adapted from Skew the Script, Lesson 5.4.