UNIVERSITY OF BOTSWANA
DEPARTMENT OF STATISTICS
STA 114: Business Statistics I
Tutorial 5
1. a) A sales person, after calling on a client, records the outcome: Sale made (S), or no sale made
(N). List the possible samples of outcomes in one afternoon if
i) Two clients are visited
ii) Three clients are visited
b) Three people are randomly selected from a voter registration and the gender of each person is
noted.
i) Define a random experiment
ii) List the sample events in S.
2. A discrete random variable X has the following probability distribution;
x
P(X=x)
0
1/8
1
3/8
2
3/8
3
1/8
a) Does it conform to probability rules?
b) Find the expected value and variance of a random variable X
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3. a) A bag contains card numbered 1,2,3,......,12. Define A to be the set of numbers smaller than 5
and B the set of numbers between 3 and 8(both numbers inclusive)
Show that A and B are independent
b) One card is randomly picked from a deck of playing cards. Are the following events mutually
exclusive?
A = The event of getting an spade.
B = The event of getting a queen
4. a) Given the following sets; S=[5,6,7........,14,15} , A={5,6,7,8,9,10}
C={11,12,13,14,15},
find: i) A Ụ B ii) B Ụ C
iii) A ∩ B
iv) A ∩ C
B={7,8,9,10,11,12},
C
iv) (AUB) ∩C
C
v) B ∩ C
C
b) Given, P(E)=0.5, P(F)=0.6, P(E∩F)=0.3. Find i) P(EUF), ii) P(F ) iii) P(E∩F )
5. Suppose two six-sided dice are thrown simultaneously.
a) Prepare a table showing all possible events that can occur
b) What is the probability that;
i)
the sum of the numbers on the two dice will be 5 or less;
ii)
the number on the second die will be 5 or more;
iii)
both dice will show the same number.
c) Are the probabilities calculated in b (i) - b(iii) above based on subjective, classical or frequentist
approach? Justify your answer
d) Show that the events in the sample space satisfy the laws of probability.
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6.
The following table gives the gender and level of education of six hundred employees at the
Tuesday Morning’s Department Store corporate headquarters in Johannesburg.
Gender\Edu
Male
Female
Total
No college college
25
225
75
275
100
500
Total
250
350
600
An employee is selected at random.
a. What is the probability that an employee is female?
b. What is the probability that an employee attended college given that she is a female employee?
c. Find the probability that the employee is a male who never attended college
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