Exam 4: Introduction to Probability

Records of a company show that 15% of the employees have only a high school diploma (H), 75% have bachelor degrees (B), and 10% have graduate degrees (G). Of those with only a high school diploma, 12% hold management positions; whereas, of those having bachelor degrees, 58% hold management positions. Finally, 82% of the employees who have graduate degrees hold management positions. a.What percentage of employees holds management positions? b.Given that a person holds a management position, what is the probability that she/he has a graduate degree?

Events A and B are mutually exclusive with P(A) = 0.3 and P(B) = 0.2. Then, P(B^c) =

Records of a company show that 20% of the employees have only a high school diploma; 70% have bachelor degrees; and 10% have graduate degrees. Of those with only a high school diploma, 10% hold management positions; whereas, of those having bachelor degrees, 40% hold management positions. Finally, 80% of the employees who have graduate degrees hold management positions. a.What percentage of employees holds management positions? b.Given that a person holds a management position, what is the probability that she/he has a graduate degree?

If P(A) = 0.4, P(B | A) = 0.35, P(A $\cup$ B) = 0.69, then P(B) =

Three applications for admission to a local university are checked, and it is determined whether each applicant is male or female. The number of sample points in this experiment is

The collection of all possible sample points in an experiment is

Forty percent of the students who enroll in a statistics course go to the statistics laboratory on a regular basis. Past data indicates that 65% of those students who use the lab on a regular basis make a grade of A in the course. On the other hand, only 10% of students who do not go to the lab on a regular basis make a grade of A. If a particular student made an A, determine the probability that she or he used the lab on a regular basis.

All the employees of ABC Company are assigned ID numbers. The ID number consists of the first letter of an employee's last name, followed by four numbers. a.How many possible different ID numbers are there? b.How many possible different ID numbers are there for employees whose last name starts with an A?

If P(A) = 0.68, P(A $\cup$ B) = 0.91, and P(A $\cap$ B) = 0.35, then P(B) =

Assume two events A and B are mutually exclusive and, furthermore, P(A) = 0.2 and P(B) = 0.4. a.Find P(A $\cap$ B). b.Find P(A $\cup$ B). c.Find P(A | B).

A perfectly balanced coin is tossed 6 times, and tails appears on all six tosses. Then, on the seventh trial

A six-sided die is tossed 3 times. The probability of observing three ones in a row is

Assume a businessman has 7 suits and 8 ties. He is planning to take 3 suits and 2 ties with him on his next business trip. How many possibilities of selection does he have?

Which of the following statements is always true?

In a recent survey about appliance ownership, 58.3% of the respondents indicated that they own Maytag appliances, while 23.9% indicated they own both Maytag and GE appliances and 70.7% said they own at least one of the two appliances. Define the events as M = Owning a Maytag appliance G = Owning a GE appliance a.What is the probability that a respondent owns a GE appliance? b.Given that a respondent owns a Maytag appliance, what is the probability that the respondent also owns a GE appliance? c.Are events "M" and "G" mutually exclusive? Why or why not? Explain, using probabilities. d.Are the two events "M" and "G" independent? Explain, using probabilities.

Each customer entering a department store will either buy or not buy some merchandise. An experiment consists of following 3 customers and determining whether or not they purchase any merchandise. The number of sample points in this experiment is

Of the last 100 customers entering a computer shop, 25 have purchased a computer. If the classical method for computing probability is used, the probability that the next customer will purchase a computer is

An applicant has applied for positions at Company A and Company B. The probability of getting an offer from Company A is 0.4, and the probability of getting an offer from Company B is 0.3. Assuming that the two job offers are independent of each other, what is the probability that a.the applicant gets an offer from both companies? b.the applicant will get at least one offer? c.the applicant will not be given an offer from either company? d.Company A does not offer her a job, but Company B does?

Two events are mutually exclusive

An experiment consists of selecting a student body president and vice president. All undergraduate students (freshmen through seniors) are eligible for these offices. How many sample points (possible outcomes as to the classifications) exist?