Student Guide: Coin Toss-up
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.
- 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.
To do this activity you will need:
- A coin (one you choose as the best for flipping)
- Data tables (below)
- Pencil (1)
- Graph paper (2 sheets)
- 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.
- 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 table below under the first column.
|4 Heads, 1 Tails|
|3 Heads, 2 Tails|
|2 Heads, 3 Tails|
|1 Heads, 4 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?