If a basketball player is a 90% free-throw shooter what are the chances he makes 106 in a row?
Chances a 90% free throw shooter makes 106 straight baskets?
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probability
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4What are your own ideas on how to approach the question? – 2012-10-13
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0If all the free throws are independent of one another, this is a binomial process. Since you're asking for the conjunction of events, 0.9^k is the probability of making k straight shots, so 0.9^106=0.0000141158 is the probability of making 106. Probability&statistics 101. – 2012-10-13
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0@PatrickLi wasn't aware that was part of the process – 2012-10-13
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0Of course the assumption that successive shots are independent is unrealistic. But that never stopped homework writers. – 2012-10-13
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0@Gedgar True. Though this one wasn't a homework question (someone added that tag), I did it once when practicing and consider myself a 90% shooter :) – 2012-10-28
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0@jim_shook That one time that you did this: did you set out to only shoot 106 times? Or was it more like, somewhere in the inside of 200 straight shots you had a 106 shot streak? Or did you just start shooting and stopped the first time you missed? Lastly, how many times have you carried out this experiment? The answers to these questions inform how you calculate and interpret the probability. – 2012-10-29
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0Thanks Jordan. I was just practicing, realized I had made like 10 in a row and decided to just see how many I could make at once. Many times I have done this (shot til I missed), and many times separately I have decided to just shoot 100 and see how many I make. Usually I am around 90 to 93. – 2012-10-29
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0@jim_shook So to illustrate the issue, here's how that affects the probability - if you just set out to practice, with no prescribed stopping point, then a person with an inherent 90% success rate actually has 100% chance of _eventually_ making 106 in a row as long as they keep at it. – 2012-10-29
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0@alex.jordan yeah that makes sense. would it take 1/.000014 times (~70,000) to do it? – 2012-10-30
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0That would roughly be an expected value for the number of shots you'd need to make. Of course it would be no guarantee. And an honest calculation would be very difficult, since each of the trials of 106 consecutive shots will not be independent. (A failure of perfect shots 1 through 106 likely means a failure of shots 2 through 107 as well.) – 2012-10-30
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Given that the shooter makes 90% of its shots, the odds it makes $n$ shots in a row is given by the formula $p = 0.9^n$. Therefore, the odds of it making 106 shots in a row is simply $0.9^{106}$, which equals roughly 0.000014, or 0.0014%.