We examine some very useful set-theory properties of probability and discuss subjective probabilities.

1. V63.0233, Theory of Probability Name:
Worksheet for Sections 2.4, 2.7 : Three Simple Propositions, Probability
July 2, 2009
as Measure of Belief
1. Find the flaws in each of the following probabilistic judgments:
(i) On Thursday, Harry has to take final examinations in psychology and economics. The prob-
ability that he will pass the psychology examination is 0.38, the probability that he will pass
both examinations is 0.23, and the probability that he will pass the psychology examination
but fail the economics examination is 0.16 (poor fellow!)
(ii) The probability that the IRS will audit my tax return is 0.17, and the probability that they
will audit either my tax return or my brother’s is 0.14.
(iii) In discussing the upcoming New York Marathon, a sports writer says the odds are 4 to 1
against an American winning the race, and 3 to 1 against a New Yorker winning the race.
(iv) The probability that the Red Sox will win the first game of the season is 0.63. The probability
that they will win their second game is 0.84, and the probability that they will win both games
is 0.45.
(v) Two single women are chosen at random. The probability that one will get married within a
year is 0.27, and the probability that both will get married within a year is 0.32.
(vi) A child goes to the doctor with a fever. The probability that she gets a shot is 0.48, the
probability that she gets medicine but no shot is 0.36, and the probability that she gets
neither is 0.12.
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2. 2. I hope to get in a round of golf during the holiday weekend. Suppose that I assign the following
probabilities to certain events:
• The probability that I will slice my opening drive into the trees is 0.62.
• The probability that I will hit at least one ball into the water is 0.69.
• The probability that I will take at least four putts on one green is 0.49.
• The probability that I will slice my opening drive into the trees and hit at least one ball into
the water is 0.37.
• The probability that I will slice my opening drive and take at least four putts on one green is
0.39.
• The probability that I will hit at least one ball into the water and take at least four putts on
one green is 0.34.
• the probability that I will slice my opening drive, hit at least one ball into the water, and
take at least four putts on one green is 0.28.
What is the probability that I will do at least one of these things?
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