Question 1:
A sample of employees were surveyed. They were asked about their loyalty to the firm, the following
are the results:
Experience in the firm
Loyalty < 1 Year 1-5 Years 6-10Years > 10 Years
Yes 10 30 57 5
No 25 15 10 30
a. What is the probability of randomly selecting an employee loyal to the firm and has 10+ years of
experience?
b. What is the probability of selecting an employee who is loyal or has less than 1 year or
experience?
c. What is the probability of selecting an employee with 10+ years of experience?
d. What is the probability of selecting an employee who is not loyal, given the employee has 10+
years of experience?
e. What is the probability of selecting an employee with 10+ years of experience or one who is not
loyal to the firm?
f. Construct a tree diagram to determine the joint probabilities.
Answers
Given :
Loyalty < 1 Year 1-5 Years 6-10Years > 10 Years
Yes 10 30 5 75
No 25 15 10 30
To Find :
a. What is the probability of randomly selecting an employee loyal to the firm and has 10+ years of experience?
b. What is the probability of selecting an employee who is loyal or has less than 1 year or experience?
c. What is the probability of selecting an employee with 10+ years of experience?
d. What is the probability of selecting an employee who is not loyal, given the employee has 10+ years of experience?
e. What is the probability of selecting an employee with 10+ years of experience or one who is not loyal to the firm?
Solution:
Loyalty < 1 Year 1-5 Years 6-10Years > 10 Years Total
Yes 10 30 5 75 120
No 25 15 10 30 80
Total 35 45 15 105 200
a. Probability of randomly selecting an employee loyal to the firm and has 10+ years of experience
= 75/200
= 3/8
= 0.375
b. Probability of selecting an employee who is loyal or has less than 1 year or experience
Loyal = 120 , less than 1 year experience = 35 both 10
120 + 35 - 10 = 145
P= 145/200 = 29/40 = 0.725
c) The probability of selecting an employee with 10+ years of experience
105/200
= 21/40
= 0.525
d. The probability of selecting an employee who is not loyal, given the employee has 10+ years of experience
= 30/105
= 2/7
e. The probability of selecting an employee with 10+ years of experience or one who is not loyal to the firm
105 + 80 - 30 = 155
P = 155/200
= 31/40
= 0.775
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