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{\Large \textbf{Sample Questions: Foundations of Probability}}%\footnote{}
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STA256 Fall 2018. Copyright information is at the end of the last page.
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\item Prove $P(A^c) = 1-P(A)$. Use the axioms of probability and the tabular format illustrated in lecture.
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\item  Prove $P(\emptyset)=0$. Use the axioms of probability and the tabular format illustrated in lecture.
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\item  Prove that if $A \subseteq B$ then $P(A) \leq P(B)$. Use the axioms of probability and the tabular format illustrated in lecture.
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\item  Prove the Addition Law: $P(A \cup B) = P(A)+P(B)-P(A\cap B)$. Use the axioms of probability and the tabular format illustrated in lecture.
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\item If 23 out of 25 are employed, what is the probability of randomly choosing an unemployed person?  The answer is a number. Circle your answer.
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\item If you roll two fair dice, what is the probability of getting a sum greater than 2? The answer is a number. Circle your answer.
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\item If you roll two fair dice, what is the probability of getting two different numbers? Your answer is a number. Circle your answer.
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\item $P(A)=0.4$, $P(B)=0.5$ and $P(A\cap B)=0.3$. What is $P(A\cup B)$? The answer is a number. Circle your answer. 
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\item Of the cars in a used car lot, 50\% have engine trouble and 50\% have transmission trouble. If 25\% have both problems and you buy a car at random, what is the probability that both the engine and transmission are okay? The answer is a number. Circle your answer. 
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\item Of the prisoners in a jail, 75\% are convited murderers and 50\% have been convicted of both murder and armed robbery. Twenty percent are in jail for offences other than murder or armed robbery. If you pick a prisoner at random, what is the probability that she is an armed robber?


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This assignment was prepared by  \href{http://www.utstat.toronto.edu/~brunner}{Jerry Brunner},
Department of Mathematical and Computational Sciences, University of Toronto. It is licensed under a 
\href{http://creativecommons.org/licenses/by-sa/3.0/deed.en_US}
     {Creative Commons Attribution - ShareAlike 3.0 Unported License}. Use any part of it as you like and share the result freely. The \LaTeX~source code is available from the course website: 
     
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\href{http://www.utstat.toronto.edu/~brunner/oldclass/256f18} {\small\texttt{http://www.utstat.toronto.edu/$^\sim$brunner/oldclass/256f18}}
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