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 & 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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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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