ACTIVITY: Coin Flipping: is it Real or Fake?

1. (Fake coin tossing.) Pretend to flip a coin 200 times – put your results (H or T for each toss) in the boxes below.

Pretend Coin Flips

X

Y

Z

2. (Real coin tossing) Now flip a quarter 200 times – put your results (H or T) in the boxes below.

Real Coin Flips

X

Y

Z

3. For a given sequence of coin tosses, we define a run as a consecutive sequence of heads or tails. So for example, if we observe the sequence

TTHHTHHHTTTTTHHHTTT

we observe a run of two tails, a run of two heads, a run of one tail, a run of three heads, and so on. Here the length of the longest run is 5, since the longest run is TTTTT and the length of this run is 5. We define the number of switches as the number of changes from H to T, or from T to H. I count a total number of six switches in the above sequence.

For each row of 20 tosses in the above two tables, compute X = the number of heads, Y = the length of the longest run of heads or tails, Z = the number of switches.

4. Collect the values of X, Y, and Z from all students in the class for the fake coin flips and the real coin flips. Place the data in the boxes below

Fake coins – values of X (number of heads)

Fake coins – values of Y (longest run)

Fake coins – values of Z (number of switches)

Real coins – values of X (number of heads)

Real coins – values of Y (longest run)

Real coins – values of Z (number of switches)

5. Compare the number of heads for the fake coin flips and the real coin flips by constructing parallel dotplots. By looking at the two histograms and calculating suitable summary statistics, explain how the numbers of heads for the real coins look different from the number of heads for the fake coins.

6. Do the same comparison using the longest run variable. Which dataset tends to have “long” runs – the fake coins or the real coins?

7. Repeat the comparison using the number of switches variable. Do you notice any differences between the histogram for the number of switches for the real coins and the number of switches for the fake coins?