Recall Exercise 11.6.17 about getting into the New York City Marathon. You plan to enter until you get in and then won’t apply again. What is the smallest number of times you would have to enter so that the probability of getting in once is above 0.50?

Data from Exercise 11.6.17

Some marathons are so popular that they use lotteries to determine who can run in them. In the 2016 New York City Marathon, about 23% of those who registered to enter through the lottery were accepted. Let’s assume this percentage stays the same in future years.