Module 1 (Version A) Solution

Total points 20/20







This module is worth 20 points. Your last submission will be used for the Enal score. You may attempt this module 5 times without penalty. After 5 attempts, each additional attempt will result in a penalty of 5% (e.g., On your 7th attempt, you obtain a score of 18 points. Then, your Enal score for this module will be 18 - (2*1) = 16 points.)




If you encounter any problems with the assignment, please email zheweisun@cs.toronto.edu with [CSC384 A4] in the subject. Be sure to include the module number and version.














































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CSC384 S19 A4 Module 1 (Version A) 2019-07-29, 7)25 PM



















M1P1 - Probability Theory







Section score 9/9




What is Bayes' Rule?
1/1



Pr(B|A) = Pr(A|B)Pr(A) / Pr(B)







Pr(B|A) = Pr(A,B)Pr(A) / Pr(B)







Pr(B|A) = Pr(B)Pr(A)




Pr(B|A) = Pr(A|B)Pr(B) / Pr(A)










[True/False] Pr(A U B) = Pr(A) + Pr(B) – Pr(A ∩ B)
1/1



True







False










[True/False] If A and B are independent, Pr(B|A) = Pr(B)
1/1



True







False










[True/False] If A and B are independent, Pr(B, A) = Pr(B)
2/2



True







False












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CSC384 S19 A4 Module 1 (Version A) 2019-07-29, 7)25 PM













[True/False] If A and B are independent, Pr(B, A) = Pr(B|A)
2/2



True







False










[True/False] Pr(A) ∈ [0,1]
1/1



True







False










[True/False] Pr(A)*P(B) ∈ [0,1]
1/1



True







False











































M1P2 - Dice Rolls







Hermione has four dice in her beaded handbag: one tetrahedron (4 sides), one hexahedron (i.e., cube, 6-sides), and two octahedra (8 sides). Hermione secretly grabs one of the four dice at random. Let S be the number of sides on the chosen die. Now, she rolls the chosen die without showing it to you. Let R be the result of the roll.




Section score 11/11
























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CSC384 S19 A4 Module 1 (Version A) 2019-07-29, 7)25 PM













What is P(S=6)?
1/1



Your answer should be between 0 and 1, rounded to 3 digits after the decimal (e.g. 0.120).

























What is P(R=4)?
1/1



Your answer should be between 0 and 1, rounded to 3 digits after the decimal (e.g. 0.120).

























What is P(S=8 | R=3)?
2/2



Your answer should be between 0 and 1, rounded to 3 digits after the decimal (e.g. 0.120).

























What is P(S=6 | R=5)?
2/2



Your answer should be between 0 and 1, rounded to 3 digits after the decimal (e.g. 0.120).

























Which die is most likely if R = 5?
2/2



S = 4







S = 6







S = 8















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CSC384 S19 A4 Module 1 (Version A)
2019-07-29, 7)25 PM















Now, Hermione rolls a tetrahedron and a hexahedron at the same time. Let A = ‘sum of two dice equals 5’







How many atomic or possible events are there in the joint
1/1



probability distribution of the rolled dice?

























What is P(A)?
2/2



Your answer should be between 0 and 1, rounded to 3 digits after the decimal (e.g. 0.120).










































































































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