Short-run proportions are often quite different from long-run probabilities.

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

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

c. Flip a coin 10 times in a row. What proportion is heads? Do this 5 times (and actually do it, don’t just write down numbers!).

Proportion for first 10 flips:

Proportion for second 10 flips:

Proportion for third 10 flips:

Proportion for fourth 10 flips:

Proportion for fifth 10 flips:

d. Do the proportions in part

(c) match the expected long-run 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?