80-110 The Nature of Mathematical Reasoning
Thursday, March 15, 2001
Quiz 6
Name: _______________________________
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State the three axioms of probability theory.
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).
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State either the definition of Conditional Probability or Bayes' Theorem.
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).
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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)?
P(Thu) = 1/7
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Let 80-110 stand for "there's 80-110 lecture today". What is the value
of P( Thu | 80-110 )?
P( Thu | 80-110 ) = 1/2
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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 ) ?
P( Thu | quiz ) = 1