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09242014, 09:42 AM  #9881  
Brodo Faggins
Join Date: Dec 2009
Location: Slovenia

Quote:
Yeah, this is spot on, no point in me posting the same thing.
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Yesterday, 12:33 AM  #9882 
Registered User
Join Date: Dec 2007

Probability theory question:
Suppose that three numbers are selected one by one, at random, and without replacement, from the set of integers {1, 2, 3, . . . , n}. What is the probability that the third number falls between the first two if the first number is smaller than the second?
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Yesterday, 01:46 AM  #9883  
Registered User
Join Date: Apr 2009
Location: Argentina

There are n(n1)(n2) different ways to select three numbers out of that set.
Suppose n_1 is the Nth number and n_2 is the Mth number, then there are only MN1 number choices left for n_3. Sum over all M, N for M > N > 0, M < or equal to n. Divide by n(n1)(n2). edit: actually that completely ignores that the first number is smaller than the second one. So, what you want is P(*that event*  n_1 < n_2) and that is P(*that event* AND n_1 < n_2)*P(n_1 < n_2) P(n_3 falls between n_1 and n_2) is what I found, now you need P(n_1 < n_2).
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