Four Queens
You divide a deck of cards in half, 26 cards each. What is the prob. obtain the four queens in the same half?
The bridges are located randomly, of course.
You can use the hypergeometric distribution to find the solution Let X be the number of queens in half bridge. X has the hypergeometric distribution with the following parameters. K = Number of elements to draw objects = 26 N = total = 52 M = number of objects a given type = 4 The mass function of probability for the hypergeometric distribution is defined as: P (X = x | N, M, K) = (MC x) * ((N - M) C (k - x)) / (NCK) for x = (0, ..., K) M - (N - K) ≤ x ≤ KP (X = 0 | N, M, K) = 0 otherwise Note that the constraints on x here are very generic and it is possible to have a value of K, N and M such that for x in (0, ..., K) P (X = x) = 0. If you have n objects and R have chose them, the number of combinations is: n! / (R! (Nr)!) This can be written as the nCr NCK is the total number of possible combinations of objects K objects from N The MC x is the number of combinations to put objects of type X given the (N - M) C (k - x) is the number of combinations of objects of type not draw. Looking at the PMF you should be able to see that it is the ratio between the number of combination of selection of items X times where interest the number of combinations of choosing K - X items from the remaining elements and it is all divided by the total number of combinations for choosing K items from n objects. The expectations of the Hypergeometric distribution is KM / N = 2 The Probability Mass Function, PMF, f (x) = P (X = x) is: P (X = 0) = 0.05522209 P (X = 1) = 0.2496999 P (X = 2) = 0.3901561 P (X = 3) = 0.2496999 P (X = 4) = 0.05522209 ← response
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