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(3 points.) A bag of k n marbles contains n marbles of each of k distinct colors. A random sample (without replacement) of k marbles is drawn. Give an expression for Pk,n, defined as the probability the sample contains exactly two colors. Hint: there are (2) possible pairs of colors, and for each color there are (2n) samples drawn from at most two colors, and this includes 2 (2) samples drawn exclusively from one or the other of the two colors, and of course there are (kn) samples overall.

(3 points.) A bag of k n marbles contains n marbles of each of k distinct colors. A random sample (without replacement) of k marbles is drawn. Give an expression for Pk,n, defined as the probability the sample contains exactly two colors. Hint: there are (2) possible pairs of colors, and for each color there are (2n) samples drawn from at most two colors, and this includes 2 (2) samples drawn exclusively from one or the other of the two colors, and of course there are (kn) samples overall.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 32E
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**(3 points.)** A bag of \(k \cdot n\) marbles contains \(n\) marbles of each of \(k\) distinct colors. A random sample (without replacement) of \(k\) marbles is drawn. Give an expression for \(p_{k,n}\), defined as the probability the sample contains exactly two colors. Hint: there are \(\binom{k}{2}\) possible pairs of colors, and for each color there are \(\binom{2n}{k}\) samples drawn from at most two colors, and this includes \(2\binom{n}{k}\) samples drawn exclusively from one or the other of the two colors, and of course there are \(\binom{kn}{k}\) samples overall.
Transcribed Image Text:**(3 points.)** A bag of \(k \cdot n\) marbles contains \(n\) marbles of each of \(k\) distinct colors. A random sample (without replacement) of \(k\) marbles is drawn. Give an expression for \(p_{k,n}\), defined as the probability the sample contains exactly two colors. Hint: there are \(\binom{k}{2}\) possible pairs of colors, and for each color there are \(\binom{2n}{k}\) samples drawn from at most two colors, and this includes \(2\binom{n}{k}\) samples drawn exclusively from one or the other of the two colors, and of course there are \(\binom{kn}{k}\) samples overall.
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