eli5: Probability of 4 holes in one in golf

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I read in a paper that the chance of getting a hole in one are 12,500 to 1. The article continued that to get 4 holes in one is (1/125000) to the power of four.

Why does the chance decrease per attempt? The universe doesn’t know you’ve had one or two or three results already so why are increasing holes in one less likely?

I see that intuitively this might be the case, but I’m not fully convinced. Part of me believes that the chance of getting any number of holes in on should be 12,500 to 1.

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Anonymous 0 Comments

>Why does the chance decrease per attempt?

* Because there is only one way to succeed (everyone gets a hole-in-one) but there are lots of ways you can fail (any single person misses their hole-in-one, then they whole things fails).
* If you only consider a single hole-in-one, how many changes are for it to fail?
* Just 1.
* But if you consider three, let’s list all the ways it can go wrong.
* 1 – All three golfers fail
* 2 – First golfer gets it but second, and third fail.
* 3 – First golfer gets it, second golfer gets it, but third fails.
* 4 -First golfer gets it, second fails, but third gets it.
* 5 -First golfer fails, second fails, but third gets it.
* 6 – First golfer fails, second gets it, third gets it.
* And how many ways can we succeed?
* All three get it
* So just one.
* So you can see for a single hole-in-one, it’s 1 chance to succeed and 1 chance to fail, so it’s 50/50
* But with three holes in a row, it’s 1 chance to succeed and 6 to fail.

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