MAT 407

EXAM 1 INFORMATION

Exam date:     Tuesday, October 11th

 

This will be a closed note, closed book exam.  Calculators are permitted.  You can expect problems in a range of difficulty, similar to class examples and homework problems.  You can expect at least one proof.

 

Sections:          1.1, 1.2, 1.3, 1.4, 1.5, 1.6

 

Office hours:   Thursday October 6th    12:30 – 3:00

 

You should be able to:

·         Identify a sample space and compute probabilities of simple and compound events.

 

 

 

In addition to studying your notes and reworking your homework problems, here are some additional practice problems:

 

1.                   Of the items produced daily by a certain factory, 40% come from line I and 60% from line II.  Line I has a defect rate of 8% while line II has a defect rate of 10%. 

a.       What is the probability that an item selected at random from the set of all items will be non-defective?

b.       Suppose an item is selected at random and found to be defective.  What is the probability that it came from line I?

 

2.                   Are two events that are independent necessarily mutually exclusive?  If so, prove it.  If not, give a counterexample.

 

3.                   A recent survey asked 100 people (59 men and 41 women) if they thought women in the armed forces should be permitted to participate in combat.  Thirty-seven of the men answered “yes” while 24 of the women answered “yes.” 

a.                   What is the probability the participant chosen at random is a woman who answered “yes”? (i.e. is a woman and answered yes.)

b.                   What portion of those who answered “yes” are women?

c.                    Is a woman more likely to answer “yes” to the question than a man is?  Justify your answer.

d.                   Are the events “The participant is a woman” and “The participant answered ‘yes’” independent?  Justify your answer with probability.

e.                    Are the events “The participant is a woman” and “The participant answered ‘yes’” mutually exclusive?  Justify your answer.

 

5.             How many different code words can be formed from the letters in HAPPINESS?

6.             On any given shift, there are 9 police officers on duty in a small town.  How many different ways are there to assign 2 officers to the park, 4 to the driving patrol and 3 to the town hall?

7.             Suppose a fast food restaurant has 15 employees. 

                a.             If all are qualified for all positions, how many ways are there to fill the positions of manager, assistant manager and trainer?   

                b.             Suppose that of the 15 employees, 6 are experienced and the rest are considered new employees.  A team of three employees is to be selected at random for the closing shift.  What is the probability that it will have 1 experienced and two new employees?