Math 115                                                         Name_____________________________

Finite Mathematics

Test 5

 

1.    A company makes metal ID tags for steel storage lockers.  The tags have 2 digits       followed by 3 letters.  How many tags are possible if

 

       a.    all letters and digits can be reused?  (4 pts)

 

 

 

 

       b.    the first digit cannot be a zero and the last letter must be an x, y, or z?      (4 pts)

 

 

 

 

 

 

2.    In how many different ways could the Seven Dwarfs (of Snow White fame) be                     lined up for a group photograph?      (4 pts)

 

 

 

 

 

 

 

3.    A ski club has 21 members, 11 men and 10 women.     (4 pts each)

 

       a.    How many different 6-member committees can be formed?

 

 

 

 

 

 

 

       b.    How many 6-member committees can be formed if there must be 3 men

              and 3 women?

 

 

 

 

 

4.    An urn contains 4 red, 3 green, and 2 blue marbles.  A random sample of 4 marbles

       is drawn.       (4 pts each)

 

       a.    In how many different ways can the sample be drawn?  (Order does not matter.)

 

 

 

 

 

 

       b.    Find the probability that the sample drawn contains the following:

 

              i)     Exactly 2 green marbles.

 

 

 

 

 

 

 

 

              ii)   At least 1 red marble.

 

 

 

 

 

 

 

 

 

 

5.    Five slips of paper numbered 1 through 5 are placed in a hat.  If 3 slips are drawn,

       replacing the slip that is drawn each time, what is the probability that no two numbers

       are the same?       (4 pts)

 

 

 

 

 

 

 

 

 

 

6.    A student takes a test with 5 multiple choice questions.  Each question has 4

       possible answers and the student, not knowing any of the answers, guesses on every        question.  What is the probability that the student will get exactly 2 correct answers? 

       Clearly identify pertinent variables.        (4 pts)

 

 

 

 

 

 

 

 

 

 

 

 

 

7.    An experiment consists of drawing a single card from a standard deck.  Aces are worth 4, face cards are worth 3, even numbered cards are worth 1, and odd numbered cards are worth –1.  Let the random variable, X,  be the  point value of the card drawn.        (4 pts each)

 

       a.    Write a probability distribution for X.

 

 

 

 

 

 

 

 

b.    Find the expected (average) value for X.

 

      

 

 

 

 

 

 

 

 

 

 

 

8.    A lottery sells 2,000 tickets at $1.00 each.  There is one first prize of $1,000. 00, and

two second prizes of $30000. each.  Find the expected value of the net winnings for one ticket.     (4 pts)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

BONUS:       A bag contains 20 chips that are identical except for color.  There are five each of red, white, green, and black chips.  If you randomly select 2 chips, what is the probability that they will be the same color?  (4 pts)