Math 3118, Section 1
Fall 2002
Class exercises for Monday, November 25

1. Consider the experiment which consists of flipping a coin 3 times.
   1. Compute the probability of each of the following outcomes. (See §7.1 for background information.)
      • 3 heads
      • 2 heads
      • 1 head
      • 0 heads
         
   2. Do this experiment 10 times. Record how many heads occur for each repetition of the experiment. Then calculate the average number of heads per repetition.
      {If you wish, use the table below to record your data.}
       
   3. Do the experiment another 10 times. Record the number of heads per repetition and calculate the average number of heads per repetition. (You may get a slightly different answer the second time . . . )
       
      (Each repetition of the experiment consists of flipping a coin 3 times.)

   Trial #

   1

   2

   3

   4

   5

   6

   7

   8

   9

   10

   * *

   *

   # heads

   # heads

   # heads

   # heads

   # heads

   # heads

   # heads

   # heads

   # heads

   # heads

   Average # of heads per repetition

   First run

   *

   ______

   ______

   ______

   ______

   ______

   ______

   ______

   ______

   ______

   ______

   ______

   * *

   *

   *

   *

   *

   *

   *

   *

   *

   *

   *

   *

   * *

   Second run

   *

   ______

   ______

   ______

   ______

   ______

   ______

   ______

   ______

   ______

   ______

   ______

   
    
2. = exercise 11.1.1 in the text (How closely does the calculated value of the expectation agree with the results of your two runs of 10 repetitions each? )
    
3. = exercise 11.1.2 from the text
    
   Suggestion: To facilitate the process of guessing the answer for  n = 10  and for general  n,  
   you might want to do the calculation for  n = 4,  and perhaps for  n = 5.
    
4. = exercise 11.1.3 from the text
    
5. = exercise 11.1.5 from the text
    
6. = exercise 11.1.6 from the text
    
   Suggestion: We can represent the process as a tree diagram:
   
    
   
    
   So, for instance, the probability of getting 0 and then eventually black is found by multiplying the probabilities from the 2 stages of the process. Thus, it is .
    
7. = exercise 11.1.7 from the text