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PracticeQuiz Prob
AP Stats
Zillions of points
Name____________________________
1. An insurance company has the following information about drivers between
16 and 18 years old. 20% are involved in accidents each year. 10% of all drivers
in this age range are A students. Among those involved in an accident, 5% are A
students.
a. What is the probability that a randomly chosen student is an A student
and is involved in an accident?
b. What is the probability that a student gets in an accident, given that
they are not an A student?
2. The chances that you will ticketed for illegal parking on campus are about 1/3.
During the last nine days, you have illegally parked every day and
have NOT been ticketed (you lucky person)! Today, on the 10th day, you
again decide to park illegally. The chances that you will be caught are:
(a) greater than 1/3 because you were not caught in the last nine days.
(b) less than 1/3 because you were not caught in the last nine days.
(c) still equal to 1/3 because the last nine days do not affect the probability.
(d) equal to 1/10 because you were not caught in the last nine days.
(e) equal to 9/10 because you were not caught in the last nine days.
3. Motor vehicles sold to individuals are classified as either cars or light trucks
(including SUVs) and as either domestic or imported. In early 2004, 69% of
vehicles sold were light trucks, 78% were domestic vehicles, and 55% were
domestic light trucks. Let A be the event that a vehicle is a light truck and B the
event that the vehicle is imported. What is the probability vehicle is an imported
car?
4. An athlete suspected of using steroids is given 2 tests that operate
independently of each other. Test A has probability 0.9 of being pos. if steroids
have been used. Test B has probability 0.8 of being pos. if steroids have been
used. What is probability that neither test is positive if steroids have been used?
5. Each of two boxes contains 20 marbles, and each marble is either black or white.
The total number of black marbles is different from the total number of white
marbles. One marble is drawn at random from each box. The probability that
both marbles are white is .21. What is the probability that both are black?
6. You decide to save money by wearing your socks as mittens too. Three are
yellow, three are red and seven are labeled "Sunday". All are mixed in your sock
drawer, you’re embarrassed to wear your "Sunday" socks as mittens, and it's too
dark to see without turning on a light and waking your dog. So you pull out
socks at random. How many must you pull out to be sure you have a pair?
7. Dre made six of seventeen free throws. How many consecutive free throws must
he make to raise his percentage to exactly 50 percent?
The following two questions refer to the following situation. All human blood can be
“ABO” typed as belonging to one of A, B, O, or AB types. The actual distribution
varies slightly among different groups of people, but for a randomly chosen person
from North America, the following are the approximate probabilities:
Blood type
O
A
B
Probability
.45
.40
.11
AB
.04
8. Consider an accident victim with type B blood. She can only receive a transfusion
from a person with type B or type O blood. What is the probability that a
randomly chosen person will be suitable donor?
(a) about .11
(b) about .04
(c) about .15
(d) about .45
(e) about .56
9. What is the probability that both people in a couple will have the SAME blood
type if matings are random with respect to blood type, i.e. one partner’s blood
type does not influence the blood type of the other partner.
(a) about .21
(b) about .16
(c) about .002
(d) about .01
(e) about .38
10. In a certain math class the following weights are assigned to required activities
as follows: class participation 12%, projects 27%, homework 11%, quizzes
12%, test one 19%, and test two 19%. Each activity is graded on a 100 point
scale. A student received 91 points for participation, 51 points for projects, 60
points for homework; 79 points for quizzes, 47 points for test one and 89 points
for test two. Compute her overall weighted average for the math class.
11. If P(A) = .45, and there are 200 equally likely outcomes in the sample space,
how many outcomes are in A?
12. You roll two fair dice, a red one and a blue one. Find the following
probabilities:
Your answers should be fractions in lowest terms.
a. P(both dice are greater than 4)
b. P(4 on the blue and an odd number on the red)
c. P(even number on the red and an odd number on the blue)
d. P( number greater than 2 on the red and less than 5 on the blue)
For problems 13-16, A whole number from 1-450 has been selected. Find the
probability of each event.
13. The number is divisible by five.
14. The number is divisible by three.
15. The number is a perfect square..
16. The number is a multiple of four.
17. How many different ways are there of answering a test with twenty multiple
choice questions, each with four choices?
18. A diner serves a blue plate special which is your choice of hamburger or chicken
sandwich, fries or chips, coke or coffee and pie or ice cream. You may pick only
one of each item. How many possible lunches are there?
19. Solve
15!
 12 !
x
20. Find the probabilities associated with the following events.
A
.07
B
.06
C
.10
D
E
F
.08
G
.33
H
.04
a. P(D)=7P(E)
b. P(E) = 3P(D)
c. P(D) = .6P(E)
d. P(D)= 5.4P(E)
21. Advanced Nails makes conductors. The probability of any of its conductors
being usable is 0.99984. What is the probability that it is not usable?
Consider the following data set:
11.6
3.1
25.2
13.9
12.4
3.7
19.1
6.8
9.4
9.5
5.9
9.5
7.8
11.6
7.4
12.6
10.6
8.5
8.7
7.9
Find the following:
22. mean
23. median
24. mode(s)
25. range
26. max
27. min
28. 1st quartile
29. 3rd quartile
30. inner quartile range(iqr)
31. standard deviation for the sample
32. construct and label a box and whisker plot
33. If a single coin is tossed seven times, what is the probability of seven tails?
34. A sales manager tells his sales force the odds of making a sale on a single are 7
to 45. What is the probability a salesman will make a sale on a single call?
35. Government data shows that 29% of the labor force has at least four years of
college and that 16% of the labor force work as laborers or operators of vehicles
or machines. Can you conclude that since .29 *.16=.0464 that 4.64% of the
labor force are college educated laborers or operators of machines or vehicles?
Explain your answer. .
Reaction
None
Mild
Strong
Within 5 minutes
420
60
20
After Five Minutes
50
330
120
Totals
Reactions to Poison Ivy. A random sample of 1000 individuals with poison ivy
allergies participated in a study to gauge their reactions to the oil from a poison ivy
plant, Oil from the poison ivy plant was rubbed on the skin of the individual. Half of
the subjects had the oil washed off within 5 minutes, the other half had the oil washed
off after five minutes. The results are summarized in the chart above. The notation
for the events will be W= washing oil off within 5 minutes, A= washing oil off after 5
minutes, N=no reaction, M= mild reaction and S= Strong reaction.
Find the following:
37. P(N)
38. P(M)
39. P(S)
40. P(N, given W)
41. P(S, given W)
42. P(N, given A)
43. P(S, given A)
44. P(N and W)
45. P(M and W)
46. P(N or M)
47. Are the events N and M mutually exclusive? Explain.
48. Are the events N and W independent? Explain.
49. The following chart shows the number of traits married couples share.
Traits in Common
Number of Married Couples
6
47
5
81
4
129
3
231
2
189
1
205
None
88
Find the following probabilities for a randomly selected couple:
a) they have less than 3 traits in common
b) they have between 2 and 5 traits in common(inclusive)
c) they have at least two traits in common
d) they have no more than two traits in common
50. Answer the following questions about rolling two dice.
a) what are all of the outcomes in the sample space?
b) what is the probability the sum of the number on the dice will be 8 or 10
c) the product of the numbers will be 12