1) The probability that all three students test positive on a drug test is 1/8. 2) The mean number of one-year-olds who do not recognize their mother's voice out of a sample of 20 is 2. 3) The probability that Jenny gets heads on the fourth coin flip is 1/2.

1. College of Engineering
Engineering Data Analysis
Math 403
Problem Set #2
(Probability)
(Department)
(Section)
Submitted by: Instructor:
Engr. Monique A. Coliat ,REE,RME

2. 1. Three randomly chosen senior high school students was administered a drug test.
Each student was evaluated as positive to the drug test (P) or negative to the drug test
(N). Assume the possible combinations of the three students drug test evaluation as PPP,
PPN, PNP, NPP, PNN, NPN, NNP, NNN. Assuming each possible combination is
equally likely, what is the probability that all three students get positive results?
a. ¼
b. ½
c. ¾
d. 1/8
2. From past experience, it is known 90% of one year old children can distinguish
their mother voice from the voice of a similar sounding female. A random sample of 20
one-year old are given this voice recognition test. Let the random variable x denote the
number of children who do not recognize their mother's voice. Find the mean of x.
a. 20
b. 2
c. 4
d. 1

3. 3. Jenny flipped a coin three times and got heads each time. What is the probability
that she gets heads on the fourth flip?
a. 1
b. 0
c. 1/16
d. ½
4. Two hundred single-sport athletes were cross-classified according to gender as
follows:
Swimmer Runner Cyclist
Male 25 60 25
Female 20 50 20
What is the probability that the athlete is male or a swimmer or both?
a. 0.550 b. 0.450 c. 0.230 d. 0.005

4. 5. Three randomly chosen senior high school students were administered a drug
test. Each student was evaluated as positive to the drug test (p) or negative to the drug
test (N). Assume the possible combinations of the three students,
Drug test evaluation as PPP, PPN, PNP, NPP, PNN, NPN, NNP, NNN.
Assuming each possible combination is equally likely, what is the probability at least one
student gets negative result?
a. 4/8
b. 2/7
c. 7/8
d. 3/7
6. A bag contains 3 red, 6 blue, 5 purple and 2 orange marbles. One marble is
selected at random. What is the probability that the marble is blue?
a. 3/8
b. 3/16
c. 3/5
d. 4/13

5. 7. In a debate on two issues among 32 people, 16 agreed with the first issue, 10
agree with the second issue and of these 7 agreed with both. What is the probability of
selecting a person at random who did not agree with either issue?
a. 1/32
b. 3/10
c. 13/32
d. 3/8
8. The plate number of a vehicle consists of 5-alphanumeric sequence is arranged
such that the first 2 characters are alphabet and the remaining 3 are digits. How many
arrangements are possible if the first character is a vowel and repetitions are not
allowed?
a. 9000
b. 90000
c. 90
d. 900

6. 9. Mark has 5 pants and 7 shirts in his closet. He wants to wear a different
pant/shirt combination each day without buying new clothes for as long as he can. How
many weeks can he do this for?
a. 4
b. 5
c. 6
d. 7
10. Twenty students enter a contest at school. The contest offers a first, second, and
third prize. How many different combinations of 1st, 2nd, and 3rd place winners can
there be?
a. 8000
b. 400
c. 6840
d. 4620

7. 11. If a series of license plates is to be produced that all have the same pattern of
three letters followed by three numbers, roughly how many alphanumeric combinations
are possible?
a. 17,576
b. 17,576,000
c. 1,757,600
d. 18,000,000
12. At an ice cream store, there are 5 flavors of ice cream: strawberry, vanilla,
chocolate, mint, and banana. How many different 3-flavor ice cream cones can be
made?
a.60
b. 10
c. 20
d. 30

8. 13. Shannon decided to go to nearby café for lunch. She can have a sandwich made
on either wheat or white bread. The café offers cheddar, Swiss, and American for
cheese choices. For meat, Shannon can choose ham, turkey, bologna, roast beef, or
salami. How many cheese and meat sandwich options does Shannon have to choose
from?
a.20
b. 10
c. 35
d. 30
14. The number of permutations of the letters of the word "ENGINEERING" is?
a.277,200
b. 25,200
c. 92,400
d. 554,400

9. 15. Find the number of ways in which 5 people A, B, C, D, and E can be seated at a
round table, such that:
(i) A and B always sit together.
(ii) C and D never sit together.