Problem 1. A fair coin is tossed repeatedly. Consider the following two possible outcomes: a) 55 or more heads in the first 100 tosses; b) 220 or more heads in the first 400 tosses. Without...

Problem 1. A fair coin is tossed repeatedly. Consider the following two possible outcomes:

a) 55 or more heads in the first 100 tosses; b) 220 or more heads in the first 400 tosses.

Without calculating, which probability is more likely? Why? Confirm this by using the normal approximation to the binomial distribution to estimate the probabilities of both events.