In a hypothetical scenario,
if Lebron James made 10 successful shots in the same spot consecutively, what is the probability that his 11 shot is successful? Is it the same probability as the 1st? or did any of his prior shots affect his 11th throw?
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What about in the instance of coin toss, similar scenario,
if i throw head for 10 times, what is the probability that i will get another head in the 11th time?
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Thanks
In: Mathematics
Depends on what assumptions you’re taking into the situation. We tend to assume coin tosses are “independent” meaning the outcome of one flip does not impact the outcome of another. So the probability of flipping heads on a fair coin on the 11th flip is 50%, regardless of the last ten flips. Those ten heads don’t give you any more information, assuming you know the coin is fair.
If you’re not sure the coin is fair, the chance of getting ten heads in a row is so low that you might want to change you assumption and question if the coin is truly fair.
You’d have a harder time arguing LeBron’s shots in a game are as independent. If LeBron is an 80% FT shooter in his career, then a decent first guess would be 80%, but if he made the last 10, I think it’s reasonable to argue he has a better than normal chance of making this. This is sometimes called “hot hands” in sports statistics, but it can be as simple as if he made the last ten, he’s really feeling good, he’s in the zone, he’s totally healthy. The 10 made FTs give you information you can use to adjust your guess. Similarly, if he missed the last ten, you probably wouldn’t guess he has an 80% chance on the eleventh, because the fact he missed ten in a row tells you he might be hurt or something.
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