Math 3118, Section 3

Spring 2001

Class exercises for Thursday, April 12 and Tuesday, April 17

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 on the back of this page 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.)

Repetition #

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.
    

[New problems for 4/17/01 start here]
 

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