AMS507 Introduction to Probability. Sample Final Test
Fall, 2009
You shall receive 5 points for each of the following 20 questions.
1. In how many ways can a man divide 7 gifts among his 3 children if
the eldest is to receive 3 gifts and the others 2 each?
2.
If
n
balls are randomly placed into
n
cells, what is the probability
that each cell will be occupied.
3.
An integer is selected at random from the set
{
1
,
2
, . . . ,
100
,
000
}
.
What is the probability that it contains the digit 4?
4. A number is selected randomly from the set
{
1
,
2
, . . . ,
1000
}
.
What is
the probability that it is divisible by 5 but not by 3?
5. From a group of 3 freshmen, 4 sophomores, 4 juniors, and 3 seniors
a committee of size 4 is randomly selected. Find the probability that the
committee will consist of 2 sophomores and 2 juniors.
6.
A number is selected at random from the set of natural numbers
{
1
,
2
, . . . ,
1000
}
.
What is the probability that it is not divisible by 5, 7, or
8?
7. You asked your neighbor to water a plant while you are on vacation.
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 Spring '08
 Feinberg,E
 Probability, Variance, Probability theory, probability density function

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