M230

Test I

Fall 1997

Bellamy

Problems #2 is worth 40 points; ten points for each part. Probelm 5 is bonus 10 point quiz. The other problems are worther 20 points each. As with any mathematics test, show all your work.

1. Write down two sets A and B, different from each other and both nonempty, with the property that A B = B. Use standard notation, listing the elements inside braces { } to specify the sets.
   
   

2. An executive has recently bought ten books; three are science fiction, two are mainstream fiction, four are management theory, and one is a how-to book about herb gardening. Since her laptop is being repaired, she chooses four of these books to read on a long flight (You may interpret these questions as either permutations or combinations but you must be consistant and either take order into account on each part or never take it into account.)
   
   
   1. How many different choices are possible?
      
   2. How many choices contain one book of each category?
      
   3. How many choices include both fiction and nonfiction?
      
   4. If all choices are equally likely, find the probability that at least one of the books chosen is science fiction.
   
   
   

3. Let M={a,b,c,d}; and let N={1,2,3}. How many elements are in each of the following sets:

   (a) M M

   (b) M N

   (c) N N

   (d) M N

   
   

4. Let A and B be events in a sample space S with Pr(A)=.45, Pr(B)=.70 and Pr(A B) = .25. Find the probability of each of the following events, using a Venn diagram.

   (a) B' A

   (b) A' B

   (c) A' B'

   (d) A' B

   
   

5. (BONUS 10 quiz points) If a hand is a five card subset of a fifty-two card deck, how many hands have exactly three of the four suits (hearts, spades, clubs, diamonds) represented?
   
   

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