Thursday, March 15, 2001

*Quiz 6*

Name: _______________________________

- State the three axioms of probability theory.
- State either the definition of Conditional Probability or Bayes' Theorem.
- 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(Thu) stands for "the probability that today is Thursday", what is the value of P(Thu)?
- Let 80-110 stand for "there's 80-110 lecture today". What is the value of P( Thu | 80-110 )?
- As you know, Thursday is Quiz-Day, so if there's a quiz then it's Thursday. What is the value of P( Thu | quiz ) ?

1. 0 <= P(A) <= 1

2. P(True)=1

3. P(A or B) = P(A)+P(B), when A and B cannot both be true at the same
time.

(Lecture, Handout #18).

Conditional Probability: P(A|B) = P(A and B) / P(B)

Bayes' Theorem: P(A|B) = ( P(B|A)*P(A) ) / P(B)

(Lecture, Handout #18).

P(Thu) = 1/7

P( Thu | 80-110 ) = 1/2

P( Thu | quiz ) = 1