MATH 210
Exam 3
November 20, 1996
1.
A red and a green die are cast. What is the probability that the sum of the numbers on the top faces is 5?(a)
1 / 6
(b)
1 / 12
(c)
1 / 18
(d)
1 / 36
(e)
None of the above.
2.
A red and a green die are cast. What is the probability that the sum of the numbers on the top faces is 5, given that the green die has a 3 on its top face?(a)
1 / 6
(b)
1 / 12
(c)
1 / 18
(d)
1 / 36
(e)
None of the above.
3.
A red and a green die are cast. What is the probability that the sum of the numbers on the top faces is 5 and the green die has a 3 on its top face?(a)
1 / 6
(b)
1 / 12
(c)
1 / 18
(d)
1 / 36
(e)
None of the above.
For the next two problems, consider the following:
A survey of a large group of people yielded the following results.
The probability that a person randomly chosen from this group is a smoker is 0.25.
The probability that a person randomly chosen from this group is a beer drinker given that the person is a smoker, is 0.8.
The probability that a person randomly chosen from this group is a beer drinker, given that the person is not a smoker, is 0.4.
4.
A person is chosen at random from the group. What is the probability that the person is a beer drinker?(a)
0.4
(b)
0.5
(c)
0.6
(d)
0.8
(e)
None of the above.
5.
A person is chosen at random from the group. The person is a beer drinker. What is the probability that the person is a smoker?(a)
0.25
(b)
0.4
(c)
0.5
(d)
0.55
(e)
None of the above.
6.
A coin is tossed 5 times. What is the probability that the number of heads is exactly 3?(a)
5/16
(b)
3/5
(c)
3/15
(d)
3/16
(e)
None of the above.
7.
An experiment consists of observing the gender and order of birth of children in families with three children.Let E be the event "the first child is a boy."
Let F be the event "the last child is a girl."
Let G be the event "the first child is a boy or the last child is a girl."
Which of the following is equal to G?
(a)
(b)
(c)
(d)
(e)
None of the above.
For the next two problems, consider the following:
A box contains 10 balls, of which 2 are red and 8 are green. A sample of 4 balls will be selected.
8.
A box contains 10 apples. Two of the apples have worms; the other eight apples are good. A sample of 3 apples is selected from the box. What is the probability that at least one apple in the sample has a worm?(a)
7/15
(b)
8/15
(c)
2/3
(d)
2/15
(e)
None of the above.
9.
If E and F are mutually exclusive events withPr(E)=1/3 and Pr(F)=1/4 then
(a)
1/12
(b)
7/12
(c)
1/7
(d)
1/2
(e)
None of the above.
10.
If E and F are independent events withPr(E)=1/3 and Pr(F)=1/4 then
(a)
1/12
(b)
7/12
(c)
1/7
(d)
1/2
(e)
None of the above.
For the next two problems consider the following:
Two brands of cola are available in Kalbville.
Right now, 60% of the population buys Brand I and 40% buys Brand II. Every year, 40% of the people buying Brand I switch to Brand II. Every year, 20% of the people buying Brand II switch to Brand I.
11.
What percent of the population of Kalbville will buy Brand I two years from now?(Round off your answer to the nearest whole percent.)
(a)
44%
(b)
56%
(c)
38%
(d)
62%
(e)
None of the above.
12.
In the long run, what percent of the population of Kalbville will buy Brand I?(Round off your answer to the nearest whole percent.)
(a)
44%
(b)
33%
(c)
67%
(d)
56%
(e)
None of the above.
13.
Consider the following matrices:
Which are stochastic and regular?
(a)
None.
(b)
U only.
(c)
V and W.
(d)
W only.
(e)
Some other selection.
14.
Which of the following are absorbing stochastic matrices?
(a)
C only.
(b)
A and B only.
(c)
A and C only.
(d)
A, B and C.
(e)
Some other selection.
15.
Consider a Markov process with transition matrix:
Which of the following is the stable matrix?
(a)
A
(b)
B
(c)
C
(d)
D
(e)
E
© Department of Mathematical Sciences, Northern Illinois University, DeKalb IL 60115
Prepared 11/11/97 by Dr. Anders Linnér (
alinner@math.niu.edu)