Description
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.
https://docs.google.com/forms/d/e/1FAIpQLSdg35GB0J37ZYH-Z48…N01G48ZvoLUpgHMQ1HfshN2RjhK-oYkROWvWoKbUR4dBkeM4C7oF8_mr_qU Page 1 of 5
CSC384 S19 A4 Module 1 (Version A) 2019-07-29, 7)25 PM
M1P1 – Probability Theory
Section score 9/9
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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)
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[True/False] Pr(A U B) = Pr(A) + Pr(B) – Pr(A ∩ B)
1/1
True
False
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[True/False] If A and B are independent, Pr(B|A) = Pr(B)
1/1
True
False
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[True/False] If A and B are independent, Pr(B, A) = Pr(B)
2/2
True
False
https://docs.google.com/forms/d/e/1FAIpQLSdg35GB0J37ZYH-Z48…N01G48ZvoLUpgHMQ1HfshN2RjhK-oYkROWvWoKbUR4dBkeM4C7oF8_mr_qU Page 2 of 5
CSC384 S19 A4 Module 1 (Version A) 2019-07-29, 7)25 PM
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[True/False] If A and B are independent, Pr(B, A) = Pr(B|A)
2/2
True
False
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[True/False] Pr(A) ∈ [0,1]
1/1
True
False
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[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
https://docs.google.com/forms/d/e/1FAIpQLSdg35GB0J37ZYH-Z48…N01G48ZvoLUpgHMQ1HfshN2RjhK-oYkROWvWoKbUR4dBkeM4C7oF8_mr_qU Page 3 of 5
CSC384 S19 A4 Module 1 (Version A) 2019-07-29, 7)25 PM
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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).
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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).
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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).
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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).
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Which die is most likely if R = 5?
2/2
S = 4
S = 6
S = 8
https://docs.google.com/forms/d/e/1FAIpQLSdg35GB0J37ZYH-Z48…N01G48ZvoLUpgHMQ1HfshN2RjhK-oYkROWvWoKbUR4dBkeM4C7oF8_mr_qU Page 4 of 5
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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’
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How many atomic or possible events are there in the joint
1/1
probability distribution of the rolled dice?
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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).
https://docs.google.com/forms/d/e/1FAIpQLSdg35GB0J37ZYH-Z48…N01G48ZvoLUpgHMQ1HfshN2RjhK-oYkROWvWoKbUR4dBkeM4C7oF8_mr_qU Page 5 of 5