1. Pretend you are flipping a fair coin. Without actuallyflipping the coin, imagine the first toss. Write down the resultyou see in your mind, heads (H) or tails (T).
2. Imagine a second coin flip. Write down the result.
3. Keep doing this until you have 50 H’s or T’s written down. Writeyour results in groups of 5 to make it easier to read, likethis:
HTHTH HHTHH (do not use these results, make your own)
4. A run is a repetition of the same result. In the example in step3, there are 2 runs of size 2 for H in the first 10 coin flips.Read through your 50 imagined coin flips, and count the number ofruns of size 2, 3, 4, etc. Record the number of runs of each sizein the table below. (Note: a run of 3 T or 3 H are both counted as3. What was actually flipped does not matter as long as it is a runof the same flip.)
RunLength 23456789 Frequency
5. Use your calculator to generate a similar list of 50 coin flips.Let 1 represent a head and 0 a tail. To do that go from the homescreen on the calculator and execute the command
randint (0,1,50)-> L1. The command randint can be found underMATH/PRB/5:randint(
6. Go to L1 and record the number of runs of size 2, 3, 4 etc. onthe table below.
RunLength 23456789 Frequency
7. Compare the two results. Did you or your calculator have thelonger run? How much longer? Compare your answers to a fewneighbors. Who had longer runs? From the Calculator or mind?
8. What can these results tell us about randomness? How good is thehuman mind at randomness? Answer this question with a well writtenparagraph at least 5 sentences long.