Exercise 25
Philosophy 102 (Maher)
Spring 2009
For now, simplify your answers just to see how big the probabilities are. But in quizzes and the
exam, you need not simplify; a correct numeric expression will be sufficient.
1. In a routine physical exam, Paul was tested for a disease that only 1 person in 10,000 has.
The characteristics of the test are that 99% of people who have the disease test positive and
2% of those who don’t have the disease test positive. Let
T
= the test result was positive,
D
= Paul has the disease. Find
p
(
D

T
).
2. A box contains 5 dice, of which four are fair but one is biased so it lands six half the time. A
die is drawn from the box and tossed twice. Let
S
= the die lands six both times,
B
= the
die is biased. Find
p
(
B

S
).
3. In a certain town, 85% of the cabs are green and the other 15% are blue. One night a cab was
involved in a hitandrun accident. A witness was tested under conditions like those on the
night of the accident and found to identify blue cabs as blue 80% of the time and to identify
green cabs as blue 20% of the time. Let
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 Spring '08
 WEINBERG
 Philosophy, Type I and type II errors, white balls, Belinda, correct numeric expression

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