80-110 The Nature of Mathematical Reasoning

Thursday, March 15, 2001

Quiz 6

Name: _______________________________

1. State the three axioms of probability theory.

2. 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).

3. State either the definition of Conditional Probability or Bayes' Theorem.

4. 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).

5. 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)?

6. P(Thu) = 1/7

7. Let 80-110 stand for "there's 80-110 lecture today". What is the value of P( Thu | 80-110 )?

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

9. 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 ) ?

10. P( Thu | quiz ) = 1