Here's a fun problem I came across. During an hour two independent events can happen at any time. What's the probability that the events are at least 10 minutes apart?

Question

rational · Answer

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kainui · Answer

Hahaha yeah you got it.

rational · Answer

P(|E1-E2| > 10 minutes) = (Area of shaded region) / (Total area) = 5^2/6^2 = 25/36  ?

kainui · Answer

Yep, exactly. =)

rational · Answer

these are really fun xD
i got some practice a couple of months ago when @amistre64 was preparing for some probability theory exam

kainui · Answer

Something that just occurred to me that I don't know the answer to is what is the probability of having 3 events 10 minutes apart?

Or, is there a good reason why the probability is 5^2/6^2? If the events were separated by 20 minutes would the answer then become 4^2/6^2 ? I guess this would be easy to check for the general answer.

rational · Answer

very interesting, 3 events requires a triple integral is it

rational · Answer

second part of the question is easy yeah 
we always get squares in top and bottom because of symmetry :  |E1-E2| > 20

kainui · Answer

for the 2D case in general the answer is:

$$\frac{(60-t)^2}{60^2}$$ which is quite nice!

parthkohli · Answer

Wow, that's beautiful.

parthkohli · Answer

Looks like my book has this... is this what is called "infinitistic probability"?

kainui · Answer

Yup, I guess? I guess continuous probability distribution maybe? It's important for quantum mechanics!

ikram002p · Answer

:)

dan815 · Answer

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