MATH 301/601, Test 1, February 8, 2006
1.
From the integers 1,...,10, three numbers are chosen at random without
replacement and disregarding the order.
(a)
In how many ways can this be done?
(b)
What is the probability that the smallest number is 4?
(c)
Do (a) and (b) with 10 replaced by an integer
n
and 4 replaced by an
integer
k
(where
n
≥
3 and
k
≤
n

2)
2.
Consider two urns such that urn I has two black balls and urn II has one
black ball and one white ball. You choose an urn at random and then pick a
ball from this urn.
(a)
If the ball is black, what is the probability that you chose urn I?
(b)
If you draw twice with replacement from the chosen urn and get two
black balls, what is the probability that you chose urn I?
(c)
If you draw
j
times with replacement from the chosen urn and only get
black balls, what is the probability that you chose urn I?
3.
Let
A
and
B
be events. Are the following statements true or false?
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 Spring '08
 staff
 Statistics, Integers, Probability, urn, black balls, Urn II

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