help Math 323 Probability Journal Name (4) 6. A. What is a hypergeometrie distri

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Math 323 Probability Journal Name (4) 6. A. What is a hypergeometrie distribution? B. Show the formula and calculate how to determine the probability of getting four blue eggs if there are 10 blue eggs in a basket and the rest are other colors if you pick 7 eggs out of 24 eggs in basket. C. Is it more likely that you will pick 4 blue eggs or 5 blue eggs if there are 10 blue eggs in a basket and the rest are other colors if you pick 7 eggs out of 24 eggs in baske D. What is the expected value of blue eggs you will choose if there are 10 blue eggs in a basket and the rest are other colors if you pick 7 eggs out of 24 eggs in basket?

Explanation / Answer

Question 6

(A) Here "HyperGeometric Distribution"  is a discrete probability distribution that describes the probability of k successes (random draws for which the object drawn has a specified feature) in n  draws, without replacement, from a finite population of size N that contains exactly K objects with that feature, wherein each draw is either a success or a failure.

(B) Here

Pr(4 blue eggs out of 7) = 10C4 * 14C3 /24C7 = 0.2209

(C) Pr(X = 4 or 5 ; 10 , 7 , 24) = 10C4 * 14C3 /24C7 + 10C5 * 14C2/24C7 = 0.2209 + 0.0663 = 0.2872

(D) Here expected number of blue eggs = 10 * 7/24 = 2.9167

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