CSCI 2011 Minneapolis Community and Technical College Computer Science Problems
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CSCI 2011 Homework 6
Chapter 10 Problems
Problem 1:
You are rolling a fair six sided die.
a) You roll it once. What is the probability you get an even number?
b) You roll it twice. What is the probability you get an even number at least once?
c) You roll it a hundred times. What is the probability you get an even number at least once?
d) Now imagine that the die was drawn randomly from a bag with six fair die and one dice weighted to always
roll a 3. How many times would you have to roll a 3 in a row before concluding the die is at least as likely to be
weighted as fair?
Problem 2:
Your company is preparing to roll out a fancy new facial recognition tool for detecting criminals from photographs,
marketed as EyeOfSauron or E.O.S. Assume that one in a hundred residents of Oceania is a criminal. Each input
photograph contains on Oceania resident. If the resident is a criminal, E.O.S. predicts correctly (CRIMINAL) with
80% probability and incorrectly (INNOCENT) with 20% probability. If the resident is not a criminal, E.O.S. predicts
correctly (INNOCENT) with 95% probability and incorrectly (CRIMINAL) with 5% probability.
Given that E.O.S. predicts a resident is CRIMINAL, what is the probability that they are actually a criminal? There
is no need to simplify fractions. (Many people guess far too high; this bias is known as base rate neglect).
Problem 3:
Which is more likely to take place:
a) The United States of America will send armed forces to join the conflict between Russia and Ukraine.
b) An accidental Russian strike on Poland will cause the Unite States of America to send armed forces to join the
conflict between Russia and Ukraine.
Explain. It may be helpful to read about the conjunction fallacy.
Optional Challenge Problem 1:
Research Coxàtheorem and explain how his postulates differ from Kolmogorovàaxioms of probability. What is
the relationship between the two?
1
Chapter 12 Problems
Problem 4:
Consider a graph G with ??, ?? ? ??(??). If there is no ?? ? ?? walk in G, can we say that there is a ?? ? ?? walk in ???
Prove your answer.
2
Purchase answer to see full
attachment
Chapter 10 Problems
Problem 1:
You are rolling a fair six sided die.
a) You roll it once. What is the probability you get an even number?
b) You roll it twice. What is the probability you get an even number at least once?
c) You roll it a hundred times. What is the probability you get an even number at least once?
d) Now imagine that the die was drawn randomly from a bag with six fair die and one dice weighted to always
roll a 3. How many times would you have to roll a 3 in a row before concluding the die is at least as likely to be
weighted as fair?
Problem 2:
Your company is preparing to roll out a fancy new facial recognition tool for detecting criminals from photographs,
marketed as EyeOfSauron or E.O.S. Assume that one in a hundred residents of Oceania is a criminal. Each input
photograph contains on Oceania resident. If the resident is a criminal, E.O.S. predicts correctly (CRIMINAL) with
80% probability and incorrectly (INNOCENT) with 20% probability. If the resident is not a criminal, E.O.S. predicts
correctly (INNOCENT) with 95% probability and incorrectly (CRIMINAL) with 5% probability.
Given that E.O.S. predicts a resident is CRIMINAL, what is the probability that they are actually a criminal? There
is no need to simplify fractions. (Many people guess far too high; this bias is known as base rate neglect).
Problem 3:
Which is more likely to take place:
a) The United States of America will send armed forces to join the conflict between Russia and Ukraine.
b) An accidental Russian strike on Poland will cause the Unite States of America to send armed forces to join the
conflict between Russia and Ukraine.
Explain. It may be helpful to read about the conjunction fallacy.
Optional Challenge Problem 1:
Research Coxàtheorem and explain how his postulates differ from Kolmogorovàaxioms of probability. What is
the relationship between the two?
1
Chapter 12 Problems
Problem 4:
Consider a graph G with ??, ?? ? ??(??). If there is no ?? ? ?? walk in G, can we say that there is a ?? ? ?? walk in ???
Prove your answer.
2
Purchase answer to see full
attachment
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