DOUBLE EVENT INVESTIGATION

Introduction

You will investigate the probability values for a double event. Flipping one coin is a single event, whereas flipping two coins at a time is a double event. So, double events occur when two things happen at the same time. In "SINGLE EVENT PROBABILITY," you tallied 50 flips of one coin. In this exercise, you will flip two coins at the same time and tally your results. Your teacher will also record the totals in a chart on the board so that more accurate probabilities can be calculated.

Procedure and Data

One partner will toss two coins fifty times and have his/her partner record the results using tally marks in the table below. Then reverse so that the person who did the tallying will now flip the coin. Have your partner record your tosses in the table below.

results will vary

                        My Results                                                 
 two heads           a head and a tail           two tails                         
                                                                                   
              My totals for each type of toss                Total number of       
                                                             tosses                
                                                                      50           

Data Analysis of Your Coin tosses

To determine the probability for each of the three situations above, divide the tally for each situation by the total number of tosses (write a fraction and then the decimal equivalent). That is:

results will vary

* Pr

* Pr

* Pr

Data Analysis of your Class's Tosses

Report your tally values to your teacher. After all students have reported their tallies, find the sum of each type of double event flip. Record the class values in the table below:

results will vary

Class totals for each type of                                        
toss                                                                 
 two heads    a head and a tail   two tails   Total class tosses  
                                                                  

Determine the "class's" probability for rolling each of the above by the formulas below:

* Pr results will vary

* Pr

* Pr

Comparison of the Two Table Results

1. Compare your class probabilities with the probabilities you arrived at after only 50 flips of the coin. Which set of values do you think are more reliable? Why?

The class probabilities are more reliable because as the number of investigations increase so does the reliability of the results.

2. The more times we flip the coins, the closer our probability results will be to the "theoretical" values. The theoretical values for two heads, or two tails is the same. The theoretical value for a combination of heads and tails is twice the value of a two head or two tail probability. Can you guess these theoretical values?

The theoretical values for the probability of two heads, or two tails is 0.25.

The theoretical value for the probability of a head and tail showing is 0.5.