Introduction to Statistics
Question 1
A class of 50 students obtained the following grades in a statistics course:
A 5 B 25 C 15 D 5
If one student is selected at random, what is the probability that
1 mark a. the student obtained a B?
2 marks b. the student obtained either a B or a C?
2 marks c. the student did not obtain a D?
2 marks d. the student did not obtain either a B or a C?
2 Mathematics 215 / Assignment 2A
Question 2
A realty company has 100 homes listed for sale. Some of these homes have
fireplaces, some have garages, and some have neither. A breakdown is
provided in the two-way classification table below.
Fireplace
( ) F
No Fireplace
( ) F
Garage
( ) G
50 30
No Garage
( ) G
10 10
a. If one of these 100 homes is selected at random,
1 mark i. what is the probability that the home selected does not have a
fireplace?
3 marks ii. what is the probability that the home selected has a fireplace or a
garage?
2 marks iii. what is the probability that the home selected has neither a
fireplace nor a garage?
2 marks iv. what is the probability that the home selected has a garage but not
a fireplace?
2 marks v. what is the probability that the home selected has a garage, given
that it has a fireplace?
Introduction to Statistics 3
4 marks b. Are the events
F
Fireplace and
G
Garage independent? Show your
proof.
2 marks c. Are the events F and G mutually exclusive? Why?
4 Mathematics 215 / Assignment 2A
Question 3
An person has applied for positions at Company A, Company B, and
Company C. The probability of obtaining an offer from Company A is 0.4,
from Company B is 0.3, and from Company C is 0.6. Assume that the three
job offers will be independent.
2 marks a. What is the probability that the person will receive job offers from all
three companies?
2 marks b. What is the probability that the person will receive a job offer from
Company B only?
2 marks c. What is the probability that the person will receive a job offer from at
least one of the three companies?
4 marks d. What is the probability that the person will receive exactly one job offer
from the three companies?
Hint: Construct a tree diagram.
Introduction to Statistics 5
Question 4
A city council consists of 7 males and 4 females. Two councilors are selected
at random to represent the city at an Elton John concert. What is the
probability that
2 marks a. both councilors are male?
5 marks b. one councilor is a male and one a female?
2 marks c. at least one councilor is a female?
Note: Express probabilities to 4 decimal places of accuracy.
Hint: Construct a tree diagram.
6 Mathematics 215 / Assignment 2A
Question 5
A machine used in a production process is set up correctly 97% of the time.
Given that the machine is set up correctly, only 5% of the items it produces
are defective, while 95% are not defective. On the other hand, if the
machine is set up incorrectly, 60% of the items it produces are defective,
while only 40% are not defective.
5 marks What is the probability that a randomly selected item from the production
process will not be defective?
Note: Express probabilities to 4 decimal places of accuracy.
Hint: Construct a tree diagram.
Introduction to Statistics 7
Question 6
5 marks In a survey of 100 business executives, 60 per cent were male and 40 per
cent were female. Seventy per cent of the male executives used a PDA
(personal digital assistant). Overall, 60 per cent of the executives used a
PDA. Construct a two-way classification table for the survey results.
8 Mathematics 215 / Assignment 2A
Question 7
You are given the probabilities listed below.
0.25
0.30
0.55
and 0.05
and 0
| 0.48
P A
P B
P C
P A C
P B C
P B A
2 marks a. Are A and B independent events? Why or why not?
2 marks b. Find P(A and B).
2 marks c. Find P(A or B).
2 marks d. Find P(A|B).
2 marks e. Are B and C mutually exclusive events? Why or why not?
3 marks f. Are B and C independent events? Provide a mathematical proof.