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6. Three fair dice are rolled. Find the probability mass function of the product of the three numbers appearing given that their sum is 5. Hint:

6. Three fair dice are rolled. Find the probability mass function of the product of the three numbers appearing given that their sum is 5. Hint:

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.2: Probability
Problem 3E: The conditional probability of E given that F occurs is P(EF)=___________. So in rolling a die the...
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6. Three fair dice are rolled. Find the probability mass function of the product of the three numbers appearing given that their sum is 5. Hint: Call the relevant pmf f(i) on the appropriate support. • First compute the number of equally likely possible rolls of three fair dice. • List all of the possible 3-tuples where the rolls add to 5. (order does not matter here). Now list the number of permutations for each of the 3-tuples that you listed. Now write down the product of the 3 rolls for each of your 3-tuples. • Let S be the event that the sum is 5, and compute Pr(S). • Let M; be the event that the product is i. Compute Pr(Sn M;). Finally compute Pr(M|S) for relevant i.
Transcribed Image Text:6. Three fair dice are rolled. Find the probability mass function of the product of the three numbers appearing given that their sum is 5. Hint: Call the relevant pmf f(i) on the appropriate support. • First compute the number of equally likely possible rolls of three fair dice. • List all of the possible 3-tuples where the rolls add to 5. (order does not matter here). Now list the number of permutations for each of the 3-tuples that you listed. Now write down the product of the 3 rolls for each of your 3-tuples. • Let S be the event that the sum is 5, and compute Pr(S). • Let M; be the event that the product is i. Compute Pr(Sn M;). Finally compute Pr(M|S) for relevant i.
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