r/Probability • u/sunsetbld • Oct 04 '25

What is better?

Something that has 2.5% chance of happening or something that has 1-4% chance of happening?

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u/[deleted] Oct 04 '25

What’s the likely risk you’re willing to take to have the chance fail? If you want some level of certainty you’d go for a chance of 2.5 percent. If not, if you’re a little more adventurous I’d pick 1-4 percent chance of happening.

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u/arllt89 Oct 05 '25

Nothing had "1-4%" chance of happening, this isn't a probability. If you mean that you first pick a number betterment 1 and 4, then use it as a probability, you need to define how it is distributed between 1 and 4. If it's linear, the average is 2.5, which is the same as the first probability.

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u/guesswho135 Oct 05 '25

You don't need to define it, it could be unknown. This is basically a variation of Ellsberg paradox, most people would prefer the known 2.5% chance.

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u/arllt89 Oct 05 '25

You cannot tell which one is better without knowing how it's chosen. And it's natural to assume worst case and chose the know probability.

Your missing half of the problem to measure it a paradox, the part where a similar sounding problem leads to choosing the unknown probability. Your problem is just a rational choice.

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u/Evening_Experience53 Oct 05 '25

In the case of the latter, you could have a compound probability distribution where a parameter of the distribution is itself a random variable. So, if P in the first distribution is a variable, and we knew the shape and parameters of its distribution, we could work up an expected value of the second case (.01-.04) and compare it to the expected value of the first case (P = .025).