MATH 210
Exam 3
April 16, 1997
1.
A red and a green die are cast. What is the probability that the sum of the numbers on the top faces is 10?(a)
1/3
(b)
1/6
(c)
1/12
(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 10, given that the green die has a 4 on its top face?(a)
1/3
(b)
1/6
(c)
1/12
(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 10 and the green die has a 4 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:
Students at DeKalb University were surveyed about where they ate on April 15 and whether they were ill on April 16.
The probability that a student ate at the dorms is 0.6.
The probability that a student ate at a restaurant is 0.3.
The probability that a student ate at home is 0.1.
The probability that a student was ill, given that the student ate at the dorms, is 0.1.
The probability that a student was ill, given that the student ate at a restaurant, is 0.05.
The probability that a student was ill, given that the student ate at home, is 0.05.
4.
A student is chosen at random. What is the probability that the student was ill on April 16?(a)
0.1
(b)
0.05
(c)
0.06
(d)
0.08
(e)
None of the above.
5.
What is the probability that a student ate at the dorms on April 15, given that the student was ill on April 16?(a)
0.75
(b)
0.6
(c)
0.8
(d)
0.85
(e)
None of the above.
6.
A coin is tossed 10 times. What is the probability that the number of heads is at least 1?(a)
9/10
(b)
1023/1024
(c)
1/1024
(d)
(10! - 1)/10!
(e)
None of the above.
7.
A coin is tossed 10 times. What is the probability that the number of heads is exactly 3?(a)
15/128
(b)
45/64
(c)
3/10
(d)
1/40
(e)
None of the above.
8.
A box contains 10 red balls, numbered from 1 through 10, and 10 green balls, numbered from 1 through 10. A ball is selected at random from the box. Let E be the event "the selected ball is red". Let F be the event "the number on the selected ball is odd". Let G be the event "the selected ball is green and the number on the selected ball is odd". Which of the following is equal to G?(a)
(b)
(c)
(d)
(e)
None of the above.
9.
A club has 25 members; 10 are men and 15 are women. A committee of 3 is selected at random from the members of the club. What is the probability that there are no women on the committee?(a)
10/25
(b)
8/225
(c)
10/115
(d)
6/115
(e)
None of the above.
10.
If E and F are independent events with Pr(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:
Currently, 40% of the residents of Kalbville smoke. Every year, 30% of smokers quit, and 10% of non-smokers start smoking.
11.
What percent of the population of Kalbville will smoke 2 years from now? (Round off your answer to the nearest tenth of a percent.)(a)
34%
(b)
30.4%
(c)
66%
(d)
69.6%
(e)
None of the above.
12.
After many years, what percent of the population of Kalbville will smoke? (Round off your answer to the nearest tenth of a percent.)(a)
25%
(b)
30%
(c)
0%
(d)
10%
(e)
None of the above.
13.
Consider the following matrices:
Which are stochastic and regular?
(a)
None.
(b)
U only.
(c)
U and W only.
(d)
W only.
(e)
Some other selection.
14.
Which of the following are absorbing stochastic matrices?
(a)
B 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 8/2/97 by Dr. Anders Linnér (
alinner@math.niu.edu)