The "Hot Hand" is the notion in sports that a player who is experiencing a string of successes is more likely than usual to have future success. There is debate in the world of sports, psychology, and statistics about whether the "hot hand" really exists, or if it's just humans searching for order in a random process. For a moment, let's assume that the Hot Hand exists, and is experienced by Stephen Curry, a basketball player for the Golden State Warriors known for his ability to hit 3 point shots. Let's assume that Curry's chances of hitting a 3 point shot depend on the results of his previous shot in the following way: if Curry has missed the previous 3 point shot, he has a 35% of making his next shot. If Curry has made the previous 3 point shot, he has a 55% chance of making his next shot. Assume that Curry makes his first 3 point shot of a game, and then shoots two more 3 point shots. Find the probability that he makes at least one of these two shots.
The "Hot Hand" is the notion in sports that a player who is experiencing a string of successes is more likely than usual to have future success.
There is debate in the world of sports, psychology, and statistics about whether the "hot hand" really exists, or if it's just humans searching for order in a random process.
For a moment, let's assume that the Hot Hand exists, and is experienced by Stephen Curry, a basketball player for the Golden State Warriors known for his ability to hit 3 point shots.
Let's assume that Curry's chances of hitting a 3 point shot depend on the results of his previous shot in the following way:
-
if Curry has missed the previous 3 point shot, he has a 35% of making his next shot.
- If Curry has made the previous 3 point shot, he has a 55% chance of making his next shot.
Assume that Curry makes his first 3 point shot of a game, and then shoots two more 3 point shots. Find the
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