# Student Guide: Coin Toss-up

### Summary

If you toss a coin, there is a fifty-fifty chance it will land tails-side up. But what if you toss it five times: can you predict how often you'll get one tails and four heads versus three tails and two heads? In this activity, use a coin and some graph paper to explore how the accuracy of predictions is influenced by sample size.

### Useful Vocabulary

**Probability:**A number that describes how likely an event is to happen.**Independence:**Two events, A and B, are independent from each other if, when A happens, it does not affect the probability of B happening.**Random process:**A process, like flipping a coin several times, where there can be several different possible results, and the different results may or may not be equally likely.**Histogram:**A graph that shows the distribution of data.

### Materials

To do this activity you will need:

- A coin (one you choose as the best for flipping)
- Data tables
- Pencil (1)
- Graph paper (2 sheets)

### Directions

- Practice flipping the coin you choose. Try to flip it the same way each time. You will use this coin for the duration of the experiment.
- Flip the coin five times and record if it's heads or tails in line 1 of Table 1. For example, a result in this series of heads, tails, heads, tails, and tails could be written as HTHTT.

Coin Flip Series # |
Results | Coin Flip Series # |
Results |

1 | 11 | ||

2 | 12 | ||

3 | 13 | ||

4 | 14 | ||

5 | 15 | ||

6 | 16 | ||

7 | 17 | ||

8 | 18 | ||

9 | 19 | ||

10 | 20 |

**Table 1.**Coin flip data

- Repeat step 2 nine more times so that lines 1 through 10 of the table record the results of each series of five coin flips.
- After you finish flipping the coin, notice that there are six combinations possible when flipping a coin. You can have: five heads; four heads and one tails; three heads and two tails; two heads and three tails; one heads and four tails; and five tails.
- Count how many you have of each combination, and record the information in the following table under the first column.

Combination | Count for Series #1-10 |
Count for Series #11-20 |
Total Count (Series #1-20) |

5 Heads | |||

4 Heads, 1 Tails | |||

3 Heads, 2 Tails | |||

2 Heads, 3 Tails | |||

1 Heads, 4 Tails | |||

5 Tails |

**Table 2.**Count data for each combination of heads and tails

- Using a sheet of graph paper, make a bar graph of the data from this table. Label the x-axis
*Combination*, and the y-axis*Count*. This kind of graph is called a histogram. - What does the graph look like? Which combination had the highest count?
- Now flip the coin five times again, repeating for ten additional series (#11 through #20), recording the heads/tails data in lines 11 through 20 of Table 1. Count how many you have of each combination, and record those numbers in Table 2 under the second column.
- In Table 2, add the numbers for each combination from the first series column and the second series column, then put the sum in the third column (Total Count), for a total of 20 series.
- Using a sheet of graph paper, make a bar graph of the data from the third column in Table 2. Label the x-axis
*Combination*, and the y-axis*Count*. What is the graph shaped like? - Do you see a difference between the histogram with ten series and the histogram with 20 series? What does this tell you about making predictions based on a small number of series?