5.50 Probability and coin flips: Short-run proportions are often quite different from long-run probabilities.

a. In your own words, explain why we would expect proportions to fluctuate in the short run, but why longrun probabilities are more predictable.

b. What is the expected long-run probability of heads if a person flips a coin many, many times? Why?

c. Flip a coin 10 times in a row. What proportion is heads? Do this 5 times. (Note: You will learn more by actually doing it, so don’t just write down numbers!) Proportion for the first 10 flips: Proportion for the second 10 flips: Proportion for the third 10 flips: Proportion for the fourth 10 flips: Proportion for the fifth 10 flips:

d. Do the proportions in part

(c) match the expected longrun probability in part (b)? Why or why not?

e. Imagine that a friend flipped a coin 10 times, got 9 out of 10 heads, and complained that the coin was biased. How would you explain to your friend the difference between short-term and long-term probability?