Practice Problems (Introduction to Probability)
1. Dr. Lane is grading her Accounting Quizzes and is beginning to think that students randomly guessed on all of the multiple choice questions without even trying to understand the questions and response options. Assuming the Quiz had 4 multiple choice questions, each with 4 response options and 1 correct answer. Hint: Think about the Multiplication Rule for Independent Events.
a. What is the probability of getting all 4 of the questions incorrect if students guessed randomly?
b. What is the probability of getting all 4 of the questions correct if students guessed randomly?
c. What is the probability of not getting all 4 of the questions correct if students guessed randomly?
2. Based on personnel records, you know that 20% of all full-time NSC Professors are from the College of Liberal Arts and Sciences and qualify for a merit raise. You also know that 50% of full-time NSC Professors are from the College of Liberal Arts and Sciences. What is the estimated probability that a full-time NSC Professor will qualify for a merit raise when they are from the College of Liberal Arts and Sciences?
3. Based on personnel records, you know that 45% of all hired full-time NSC Professors stay with NSC long enough to qualify for Tenure and 60% of these Professors achieve Tenure. What is the probability that any given hired full-time NSC Professor will stay long enough to qualify for Tenure and achieve Tenure?
4. Micron Technology has sales offices located in four cities: Folsom, Houston, San Jose, and Sunnyvale. The data below shows the number of overdue invoices by days for each location.
|
Days Overdue
|
Folsom
|
Houston
|
San Jose
|
Sunnyvale
|
|
Under 30 Days
|
137
|
122
|
198
|
287
|
|
30-60 Days
|
85
|
46
|
76
|
109
|
|
61-90 Days
|
33
|
27
|
55
|
48
|
|
Over 90 Days
|
18
|
32
|
45
|
66
|
a. Based on the data, what is the probability that a randomly selected overdue invoice will be from the San Jose office?
b. What proportion of invoices are between 30-60 days overdue or61-90 days overdue?
c. Based on the data, what is the probability that a randomly selected invoice from the database will be over 90 overdue and from the Houston office?
d. What proportion of overdue invoices are from Sunnyvale or are under 30 days overdue?
e. What is the probability that an invoice will be under 30 days overdue when it is from the Sunnyvale office?
f. What is the probability that an invoice will be from Sunnyvale when it is under 30 days overdue?
g. If Micron Technology randomly selected 3 invoices, what is the percent chance that all 3 are over 90 days overdue?