Will someone hit this softball out of the park?

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SUMMARY

The probability of an event that statistically occurs once in 207 attempts happening three times in 66 occurrences is calculated using the binomial probability formula. The result is approximately 1 in 263, derived from the binomial coefficient and the probabilities of success and failure. Specifically, the binomial coefficient indicates there are 45,760 different arrangements of 3 successful outcomes ("hits") and 63 unsuccessful outcomes ("misses"). This analysis provides a clear mathematical framework for understanding such probabilities.

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feveredego
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What are the odds of something that statistically should happen 1 in 207 times happening 3 times in 66 occurrences? Let me know.
 
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Short answer:
[tex]p=\binom{66}{3}(\frac{1}{207})^{3}(\frac{206}{207})^{63}\approx\frac{1}{263}[/tex]
The probability for a single, specific arrangement is [tex](\frac{1}{207})^{3}(\frac{206}{207})^{63}[/tex]
the binomial coefficient tells us how many such arrangements exist (in your case, 45760 different arrangements of 3 "hits" and 63 "misses")
Welcome to PF!
 
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