Exercise 1
Suppose that we have a sample space with five equally likely experimental outcomes : E1,E2,E3,E4,E5.
Let
A = {E1,E2}
B = {E3,E4}
C = {E2,E3,E5}
a. Find P(A), P(B), P(C).
b. Find P(A U B) . Are A and B mutually exclusive?
c. Find Ac, Bc, P(Ac), P(Bc).
d. Find A U Bc and P(A U Bc)
e. Find P(B U C)

Exercise 2
A committee with two members is to be selected from a collection of 30 people, of whom 10 are males and 20 are females.
a. Find the probability that both members are male
b. Find the probability that both members are female
c. Find the probability that one member is male and one is female.

Exercise 3
A warehouse contains 100 tires, of which 5 are defective.
Four tires are chosen at random for a new car.
Find the probability that all four are good.

Exercise 4
In a particular city,
40% of the people subscribe to magazine A, 30% of the people subscribe to magazine B and 50% to magazine C.
However, 10% subscribe to both A and B, 25% subscribe to both A and C, 15% subscribe to both B and C. Finally, 5% subscribe to all three magazines.
A person is chosen at random.
a. What is the probability that the chosen person subscribes to at least one magazine? b. What is the probability that the chosen person subscribes to at least two magazines? c. Find the conditional probability that a person subscribes to magazine A given that he or she subscribes to magazine B.

Exercise 5
Let us consider a student who is taking two tests on a given day. Let A be the event that the student passes the first test and B be the event that he passes the second.
Suppose that :
P(A) = 0.6

P(B) = 0.8

P(A ∩ B) = 0.5

a. Find the probability that the student passes the second test given that he passes the first b. Find the probability that the student passes the first test given that he passes the second

...be infected?
The probability that Alice’s RSA signature on a document is forged is () What is the probability that out of 4 messages sent by Alice to Bob at least one is not forged?
Event A is selecting a “red” card from a standard deck at random. Suggest another event (Event B) that is compatible with Event A.
What is the probability of getting 6 tails in 10 trials of tossing a coin? Solve this problem by using :The approximation mentioned in Theorem 6
The...

...continuous randomvariable because the time is being measured. All possible results for the variable time (t) would be greater than > 0.
b) The weight of a T-bone steak is a continuous randomvariable because the weight of the steak is measured. All the possible results for the weight of the T-bone steak would be positive numbers making the variable weight (w) > greater than 0....

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Turn over
2206-7303
0516
–6–
5.
M06/5/MATME/SP1/ENG/TZ2/XX
The probability distribution of the discrete randomvariable X is given by the following table.
x
1
2
3
4
5
P ( X = x)
0.4
p
0.2
0.07
0.02
(a)
Find the value of p.
(b)
Calculate the expected value of X....

...Answer: .5006
. Question 5 .5 out of 5 points
An automotive center keeps tracks of customer complaints received each week. The probability distribution for complaints can be represented as a table or a graph, both shown below. The randomvariable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.
xi
0
1
2
3
4
5
6
p(xi)
.15
.1
.28
.20
.10
.10
.07
What is the expected number of...

...Discrete RandomVariables: Homework
Exercise 1
Complete the PDF and answer the questions.
|X |P(X = x) |X(P(X = x) |
|0 |0.3 | |
|1 |0.2 | |
|2 | | |
|3 |0.4 | |
a. Find the probability that X = 2.
b. Find the expected value.
Exercise 2
Suppose that you are offered the following...

...Chapter - Section | Problem(s) |
5 – 2 | 10, 14 |
5 – 3 | 12, 32 |
5 – 4 | 18 |
5-2 #10,14
10. Eye Color Groups of five babies are randomly selected. In each group, the randomvariable x is the number of babies with green eyes (based on data from a study by Dr. Sorita Soni at Indiana University). (The symbol 0+ denotes a positive probability value that is very small).
X | P(x) |
0 | .528 |
1 | .360 |
2 | .098 |
3 | .013 |
4 | .001 |
5 | 0+ |...

...selected at random from the sample.
a) What is the probability the person is female or occasionally involved in charity work?
b) Are the events “being female and occasionally involved in charity work” and “being frequently involved in charity work” mutually exclusive?
yes
6. A company gave psychological tests to perspective employees. The randomvariable x represents the possible test scores.
a) Use the histogram to find...

...Math 107 002
Homework 5 (due 13 Oct 2011)
Fall 2011
Please use your calculators and give your ﬁnal answers to 3 signiﬁcant ﬁgures. Show your work for full credit. Please state clearly all assumptions made.
1. Classify each randomvariable as discrete or continuous. (a) The number of visitors to the Museum of Science in Boston on a randomly selected day. (b) The camber-angle adjustment necessary for a front-end alignment. (c) The total number of pixels in a...

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