MAT 407

Hand-in assignment #2

Due: Thursday, September 29th

You may hand it in in class or put it in my mailbox by 4:00.

 

Please work independently on the following problems.  Please write them up neatly, showing all your work, on separate paper and staple multiple pages together.

 

1.                  Consider the following experiment: two fair four-sided dice (called tetrahedral dice) are rolled and the pair of numbers on the upturned faces is recorded.  Suppose one die is red and the other is green.

a.   How many outcomes are there in the sample space for this experiment?  List them.

b.      Find the probabilities of the following events:

A: the red die shows a 3 and the green die shows a 2.

B: both dice show the same number.

C: the sum on the dice is equal to 5.

     

2.                  Given that, and, find  and.

 

3.                  Prove that.  Suggestion: rewrite the set difference in terms of an intersection.

 

 

4.                  Clinic records show that 28% of all patients coming in have strep throat and 51% of all patients have an allergy.  Included in those numbers are the 10% of patients that have both strep throat and an allergy.

 

a.                   What is the probability that a patient has at least one of these two problems?

b.                  What proportion of those with strep throat also have an allergy?

c.                   What proportion of those with an allergy also have strep?

d.                  Are the events “has strep throat” and “has an allergy” mutually exclusive?  Why or why not?

e.                   Are the events “has strep throat” and “has an allergy” independent?  Justify your answer with probability.

 

 

5.                  How many ways can three outfielders and four infielders be chosen from a pool of six outfielders and seven infielders?  Show your work and explain why you chose your method.

 

 

 

6.                  Nine books are to be lined up on a shelf for a display.  Two have red covers, three have green covers and the rest have blue covers.  Considering only color, how many distinguishable arrangements of the books on the shelf are possible?

 

 

7.                  A local political club consists of 5 Republicans, 7 Democrats and 4 Independents.

a.                   How many ways are there to fill the positions of President, VP, secretary and treasurer of the club?

b.                  How many different three-member committees are there?

c.                   If a three-member committee were selected at random from the club membership, what is the probability it would contain one member from each party?

d.                  If a three-member committee were selected at random, what is the probability it would contain 1 Republican, 2 Democrats and no Independents?