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An urn contains m red and n white balls. (a) We draw two
Chapter , Problem 51(choose chapter or problem)
An urn contains m red and n white balls. (a) We draw two balls randomly and simultaneously. Describe the sample space and calculate the probability that the selected balls are of different color, by using two approaches: a counting approach based on the discrete uniform law, and a sequential approach based on the multiplication rule. (b) We roll a fair 3-sided die whose faces are labeled 1 ,2,3, and if k comes up. we remove k balls from the urn at random and put them aside. Describe the sample space and calculate the probability that all of the balls drawn are red. using a divide-and-conquer approach and the total probability theorem.
Questions & Answers
QUESTION:
An urn contains m red and n white balls. (a) We draw two balls randomly and simultaneously. Describe the sample space and calculate the probability that the selected balls are of different color, by using two approaches: a counting approach based on the discrete uniform law, and a sequential approach based on the multiplication rule. (b) We roll a fair 3-sided die whose faces are labeled 1 ,2,3, and if k comes up. we remove k balls from the urn at random and put them aside. Describe the sample space and calculate the probability that all of the balls drawn are red. using a divide-and-conquer approach and the total probability theorem.
ANSWER:Step 1 of 2
a) Sample Space of the urn containing m red and n white balls,
Probability of choosing balls of different colors based on sequential approach (Multiplication Rule) is calculated as,
