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. 

a. Suppose you plan to enter the lottery for the next 5 years. What is your probability of gaining entry into the marathon exactly once? 

b. Suppose you plan to enter the lottery for the next 5 years. What is your probability of gaining entry into the marathon at least once? 

c. Suppose you plan to enter the lottery until you gain entry and then won’t apply again. What is the probability that it takes 5 years until you get in? 

d. Suppose you plan to enter the lottery until you gain entry and then won’t apply again. What is the probability that it takes 5 years or less until you get in?