Statistics/Probability Quiz

[Ether]

Originally Posted by Hitchhiker 42

= 3.55*10^(-52)

Try your computation method for the greatly simplified case of an imaginary fair 4-sided die* being rolled 8 times, and getting exactly 2 of each (1,2,3,4).

Then compare your answer to the actual answer which can easily be brute-force computed with a simple C program to be 2520/65536.



* for a 4-sided die, the value for each roll would be the side facing downward

[Basel A]

It's relatively straightforward to determine the probability that exactly 70 of the 420 rolls are ones (a simple binomial distribution problem). Next, it's relatively straightforward to determine the probability that exactly 70 of the remaining 350 are twos, etc. Using this method, I calculated the probability to be 5.9960458e-7.

[smitikshah]

Originally Posted by Basel A

It's relatively straightforward to determine the probability that exactly 70 of the 420 rolls are ones (a simple binomial distribution problem). Next, it's relatively straightforward to determine the probability that exactly 70 of the remaining 350 are twos, etc. Using this method, I calculated the probability to be 5.9960458e-7.

Ahh whoops I see my error. I just did binomial for all of them without subtracting 70 each time like a fool.

Now I got 5.99*10^-7 as well. Weird - I thought it would need to be much closer to 0.

[Ether]

Originally Posted by GeeTwo

...I get 5.99 x 10^-7...

Originally Posted by Basel A

...5.9960458e-7...

Nice work guys.

[smitikshah]

Originally Posted by Ether

Nice work guys.

Was there a certain reason for this question? Just wondering - seems a bit random.

[Ether]

Originally Posted by smitikshah

Was there a certain reason for this question? Just wondering - seems a bit random.

Just a summer diversion.

Hopefully there's a student or two out there in CD land who was inspired by this discussion to do a bit of summer reading about statistics and/or probability.

[Hitchhiker 42]

Originally Posted by Ether

Just a summer diversion.

Hopefully there's a student or two out there in CD land who was inspired by this discussion to do a bit of summer reading about statistics and/or probability.

Probably me now. I've got a Cartoon Guide to Stats that I should pick up this summer.

[GeeTwo]

If you're interested in looking for other quizzes, just search for threads with Quiz in the title (on advanced search). Ether has a bunch of them, ranging over Math, Physics, and even Geekdom, and there are a bunch of others out there as well.

[Caleb Sykes]

Originally Posted by smitikshah

Was there a certain reason for this question? Just wondering - seems a bit random.

It had to be random or it wouldn't have been a probability question.