COMP 233 Probability and Statistics for Computer Science [FINAL EXAM ACTUAL
QUESTIONS AND ANSWERS] 2025 NEW Concordia University
Q1: A system is composed of four components, each of which is either working or failed.
Consider an experiment that consists of observing the status of each component, and let the
outcome of the experiment be given by the vector (x1; x2; x3; x4) where xi is equal to 1 if
component i is working and is equal to 0 if component i is failed.
a) How many outcomes are in the sample space of this experiment?
b) Suppose that the system will work if components 1 and 2 are both working, or if
components 3 and 4 are both working. Specify all the outcomes in the event that the
system works.
c) Let E be the event that components 1 and 3 are both failed. How many outcomes are
contained in event E?
Solution:
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Q2: Each of 2 balls is painted black or gold and then placed in an urn. Suppose that each ball
is colored black with probability 0.5, and that these events are independent.
, a) Suppose that you obtain information that the gold paint has been used (and thus at
least one of the balls is painted gold). Compute the conditional probability that both
balls are painted gold.
b) Suppose, now, that the urn tips over and 1 ball falls out. It is painted gold. What is
the probability that both balls are gold in this case?
Solution:
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Q3: While at Manchester United Football Club in England, Cristiano Ronaldo had about an
80% success rate of scoring penalty goals from his penalty kick attempts from the penalty
spot. Assuming he kept scoring penalties at the same rate, and that all penalty kicks are
independent, answer the following questions:
QUESTIONS AND ANSWERS] 2025 NEW Concordia University
Q1: A system is composed of four components, each of which is either working or failed.
Consider an experiment that consists of observing the status of each component, and let the
outcome of the experiment be given by the vector (x1; x2; x3; x4) where xi is equal to 1 if
component i is working and is equal to 0 if component i is failed.
a) How many outcomes are in the sample space of this experiment?
b) Suppose that the system will work if components 1 and 2 are both working, or if
components 3 and 4 are both working. Specify all the outcomes in the event that the
system works.
c) Let E be the event that components 1 and 3 are both failed. How many outcomes are
contained in event E?
Solution:
#############################################
Q2: Each of 2 balls is painted black or gold and then placed in an urn. Suppose that each ball
is colored black with probability 0.5, and that these events are independent.
, a) Suppose that you obtain information that the gold paint has been used (and thus at
least one of the balls is painted gold). Compute the conditional probability that both
balls are painted gold.
b) Suppose, now, that the urn tips over and 1 ball falls out. It is painted gold. What is
the probability that both balls are gold in this case?
Solution:
####################################################
Q3: While at Manchester United Football Club in England, Cristiano Ronaldo had about an
80% success rate of scoring penalty goals from his penalty kick attempts from the penalty
spot. Assuming he kept scoring penalties at the same rate, and that all penalty kicks are
independent, answer the following questions:
