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Math 55 Worksheet
July 28, 2011
Adapted from worksheets by Rob Bayer, Summer 2009.
Warmups
1. If you roll 3 fair dice, what is the expected value of the sum of the dice?
Problems Proper
1. What is the probability of getting exactly 3 heads when ﬂipping a coin 5 times if the coin is twice as likely to
come up heads as tails?
2. Suppose you have 3 fair dice and 1 loaded die that comes up 6 with probability
1
3
and each other value with
probability
2
15
. If you pick a die from this set at random, roll it twice, and get a 6 twice, what’s the probability
that you picked the loaded die?
3. A test for the Common Banana Virus is 98% speciﬁc (that is, 98% of the time the test will be negative for
someone without the disease, and the remaining 2% of the time it will give a false positive) and 99% sensitive
(ie, 99% of the time the test will be positive for someone who has the disease, and 1% of the time the test gives
a false negative). Just 1% of the population carries CBV.
(a) If you test positve, what’s the probability that you actually have CBV?
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 Summer '09
 RobBayer
 Math, Probability

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