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Discrete
Probability
Distributions
1.A group of people were asked if they had run a red light in the last year. 446 responded “yes”, and 344 responded “no”.
Find the probability that if a person is chosen at random, they have run a red light in the last year.
Give your answer as a fraction
or decimal to 4 decimal places
2. A random variable is defined as a process or variable with a numerical outcome. Which of the following are random variables?
The amount of rain, in inches, that will fall next Friday in Dallas, TX.
The major of a randomly drawn student from Arizona State University.
The number of books purchased next year by your local library.
i only
ii only
iii only
i and iii
ii and iii
i, ii, and iii
3. For families with 5 children, let XX be the number of children with Genetic Condition B. Can the following table be a probability distribution for the random variable XX?
xx
P(x)
P(x)
1
0.2
842
2
0.0923
3
0.2544
4
0.1
366
5
0.1097
· no
· yes
4. Assume that 12 jurors are randomly selected from a population in which 71% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities.
xx
P(x)P(x)
0
0+
1
0+
2
0.0001
3
0.0011
4
0.0063
5
0.0246
6
0.0704
7
0.1477
8
0.2261
9
0.246
10
0.1807
11
0.0804
12
0.0164
Find the probability of exactly 7 Mexican-Americans among 12 jurors. Round your answer to four decimal places.
P(x=7)=P(x=7)=
Find the probability of 7 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places.
P(x≤7)=P(x≤7)=
Does 7 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans?
· yes
· no
5.
Probability
Scores
0.05
3
0.45
8
0.05
10
0.3
5
12
0.1
13
Find the expected value of the above random variable.
6. On a 9 question multiple-choice test, where each question has 3 answers, what would be the probability of getting at least one question wrong?
Give your answer as a fraction
7. Giving a test to a group of students, the grades and gender are summarized below
A
B
C
Total
Male
7
10
2
19
Female
17
16
18
51
Total
24
26
20
70
If one student was chosen at random,
find the probability that the student got a B.
Give your answer as a fraction or decimal.
8. The table summarizes results from 989 pedestrian deaths that were caused by automobile accidents.
Driver
Intoxicated?
Pedestrian Intoxicated?
Yes
No
Yes
45
75
No
281
588
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was not intoxicated.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the “%” symbol.
prob = %
9. Determine whether this table represents a probability distribution.
x
P(x)
0
0.2
1
0.15
2
0.3
3
0.35
· No, it is not a probability distribution
· Yes, it is a probability distribution
10.
x
P(x)
0
0.3
1
0.1
2
0.05
3
0.55
Find the mean of this probability distribution. Round your answer to one decimal place.
Discrete Probability Distributions
Discrete Probability Distributions
1
.
A
group of people were asked if they had run a red light in the last year.
4
4
6
responded “yes”, and
3
44 responded “no”.
Find the probability that if a person is chosen at random, they have run a red light in the last year.
Give your answer as a fraction or decimal to 4 decimal places
2
. A random variable is defined as a process or variable with a numerical outcome. Which of the following are random variables?
The amount of rain, in inches, that will fall ne
x
t Friday in Dallas, TX.
The major of a randomly drawn student from Arizona State University.
The number of books purchased next year by your local library.
i only
ii only
iii only
i and iii
ii and iii
i, ii, and iii
3. For families with
5
children, let XX be the number of children with Genetic
C
ondition
B
. Can the following table be a probability distribution for the random variable XX?
|
|
xx
|
|
P(x)
P(x)
|
|
|
|
|
1
|
0
.2
8
42
|
|
|
|
|
|
2
|
0.0
9
23
|
|
|
|
|
|
3
|
0.2
544
|
|
|
4
|
0.1
366
|
|
|
5
|
0.
10
9
7
|
· no
· yes
4. Assume that
12
jurors are randomly selected from a population in which 71% of the people are Mexican-Americans. Refer to the probability distribution table below and find the indicated probabilities.
xx
P(x)P(x)
|
|
|
0
|
|
0+
|
1
0+
2
|
0.0001
|
3
|
0.00
11
|
4
|
0.0063
|
5
|
0.0
24
6
|
|
6
|
0.0
70
4
|
|
|
7
|
0.1477
|
|
|
8
|
0.2
26
1
|
|
9
|
0.246
|
|
|
|
10
|
0.
18
07
|
|
11
|
0.0804
|
|
|
12
|
0.0
16
4
|
Find the probability of exactly 7 Mexican-Americans among 12 jurors. Round your answer to four decimal places.
P(x=7)=P(x=7)=
Find the probability of 7 or fewer Mexican-Americans among 12 jurors. Round your answer to four decimal places.
P(x≤7)=P(x≤7)=
Does 7 Mexican-Americans among 12 jurors suggest that the selection process discriminates against Mexican-Americans?
· yes
· no
5.
|
Probability
|
Scores
|
|
|
|
0.05
|
3
|
0.
45
|
8
0.05
10
|
|
0.3
5
|
12
|
|
0.1
|
13
|
Find the expected value of the above random variable.
6. On a 9 question multiple-choice test, where each question has 3 answers, what would be the probability of getting at least one question wrong?
Give your answer as a fraction
7. Giving a test to a group of students, the grades and gender are summarized below
|
A
|
B
|
C
|
|
Total
|
|
Male
|
7
10
2
19
|
|
Female
|
17
|
16
|
18
|
51
|
Total
|
24
|
26
|
20
|
70
|
If one student was chosen at random,
find the probability that the student got a B.
Give your answer as a fraction or decimal.
8. The table summarizes results from 989 pedestrian deaths that were caused by automobile accidents.
|
Driver
Intoxicated?
|
Pedestrian Intoxicated?
|
|
|
Yes
|
|
No
|
Yes
|
45
|
75
|
No
|
281
|
588
|
If one of the pedestrian deaths is randomly selected, find the probability that the pedestrian was not intoxicated or the driver was not intoxicated.
Report the answer as a percent rounded to one decimal place accuracy. You need not enter the “%” symbol.
prob = %
9. Determine whether this table represents a probability distribution.
|
|
x
|
|
P(x)
|
0
|
0.2
|
1
|
0.15
|
2
|
|
0.3
|
3
0.35
· No, it is not a probability distribution
· Yes, it is a probability distribution
10.
x
P(x)
0
0.3
1
0.1
2
0.05
3
|
0.55
|
Find the mean of this probability distribution. Round your answer to one decimal place.
