1. Which of the above versions of the "law of averages" are correct interpretations of probability?
2. Here is a sequence of flips of a fair coin:
a. How many heads would you expect to have after 10 flips of a fair coin? ("Expect" is a technical term that means about the same as "average." This question means, "On the average, how many heads do people get after flipping a coin 10 times?")
b. In the sequence above, what is the actual number of heads after 10 flips? What is the percentage of heads after 10 flips?
c. How many heads would you expect to have after 50 flips of a fair coin?
d. In the sequence above, what is the actual number of heads after 50 flips? What is the percentage of heads after 50 flips?
What many people find counterintuitive about the answers to question #3 is that the percentage of heads gets closer to 50% while the actual number of heads gets fur~ ther away from half the total number of flips. In fact, the law of large numbers tells us that this is what we can expect.