
Assume you woke up this morning and had no idea whatsoever about what
day of the week it was. It could be any of { Mon, Tue, Wed,
Thu, Fri, Sat, Sun }. If P(Mon) stands for "the probability
that today is Monday", what is the value of P(Mon)?
P(Mon) = 1/7.

a) As you know, there's always a quiz on Tuesdays and Thursdays, so what
is P( quiz  Tue ) ?
b) Since there is a quiz today, what is the probability that today is
Thursday, i.e, P( Thu  quiz ) ?
a) P( quiz  Tue ) = 1
b) P( Thu 
quiz ) = 1/2.

What does the following expression mean in English "P( Sun  ~quiz )",
where "~" stands for "not"?
The probability that it is Sunday, given
that there is not a quiz today.

State the three axioms of probability theory.
1) 0 <= P(A) <= 1
2) P(W)=P(T)=1
3) P(A v B) = P(A) + P(B), if A and B are incompatible
propositions. (Lecture 7/24/00 and Handout #18)

State either the definition of Conditional Probability or Bayes' Theorem.
Conditional Probability: P(A  B)= P(A & B) / P(B), where P(B)>0.
Bayes' Theorem: P(A  B) = P(B  A) * P(A) / P(B).
(Lecture 7/24/00 and Handout #18)