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.
In: 1
I’ll answer this from an intuitive perspective rather than mathematical.
Let’s say you’re at a party with a bunch of strangers. You get drunk and you begin betting people that if they could guess your name correctly by whispering it in your ear, that you’ll give them ten dollars. It’s against the rules for others to share your name with anyone else.
In one scenario, the first person guesses correctly but all subsequent guesses are wrong. One would be reasonable to assume the first attempt was a lucky guess.
In the next scenario, all guesses are correct. One would be reasonable to assume that the participants were cheating.
You could say that any given guess would be independent of one another, but intuitively the pattern of multiple correct guesses might indicate unfair play.
From a mathematically minded perspective, we can look at this a different way. Basically, successive attempts at something increases the total number of outcomes, therefore decreasing the chance of any specific outcome. For example, if you flip a coin once , you can either get heads or tails. Flip it twice? Well now you can have h/h, h/t, t/h, or t/t. There is only one outcome out of four that you have heads twice in a row.
Applying this your example probability, only one outcome out of 12500 is a hole in one. When attempting four? Well, that’s only one outcome out of 12500*12500*12500*12500. this is because we expand the set of possible outcomes, all of which except one include a failure to achieve a hole in one.
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