# A4 Module 1 (Version A) Solution

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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

 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

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

 [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

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

 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

https://docs.google.com/forms/d/e/1FAIpQLSdg35GB0J37ZYH-Z48…N01G48ZvoLUpgHMQ1HfshN2RjhK-oYkROWvWoKbUR4dBkeM4C7oF8_mr_qU Page 4 of 5

 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).

https://docs.google.com/forms/d/e/1FAIpQLSdg35GB0J37ZYH-Z48…N01G48ZvoLUpgHMQ1HfshN2RjhK-oYkROWvWoKbUR4dBkeM4C7oF8_mr_qU Page 5 of 5