Fall 2002 Math 218 Final Examination
J. Cvitanic, L. Goldstein, L. Goukasian, C. Haskell, I. Kukavica, S. Lototsky, R. Mikulevicius, E. Verona,
and Z. Vorel
Problem
1
.
In a large population, 1% of individuals are infected with a certain virus, say
V
.
A test is
applied to the whole population, and it is assumed that 99% of infected individuals test positive while 2% of
noninfected individuals test positive. Let
A
be the event that a randomly chosen individual is infected with
the virus
V
, and let
B
be the event that a randomly chosen individual tests positive for
V
.
a) Construct a probability tree diagram describing this situation.
b) Are events
A
and
B
independent? (Show your work.)
c) For events
A
and
B
in the previous problem, find
P
(
A

B
) and
P
(
A

B
).
d) Two randomly chosen individuals that are not infected with
V
are going to take this test. Find the
probability that both of them will test positive for
V
.
Problem
2
.
A box contains 5 quarters, 4 dimes, and 2 nickels.
a) We select 8 coins randomly without replacement. Find the probability that 4 or more of the selected
coins are quarters.
b) A coin is drawn randomly 5 times with replacement. Find the probability that we get at least one
quarter.
c) A coin is drawn 100 times with replacement. Find the probability that a quarter appears 50 or more
times.
Problem
3
.
Customer arrivals to the LastMinuteHolidayShoppingStore follow a Poisson distribution with
the rate of 2 per hour.
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 Fall '06
 Haskell
 Math, Normal Distribution, Probability, Variance, Probability theory, probability density function

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