With the recent launch of Artemis there has been a new initiative to send manned missions to the Moon in hopes of one day colonizing it. The newly founded International Space Agency has decided to select one lucky person from the general population to join this venture. Instead of choosing people at random, however, they decide to administer a 50-question multiple-choice test to everyone who applies. Each question has only two choices (A or B) and only one correct answer. Answer the questions below and explain the steps you used to arrive at your answers (e.g., give calculations when applicable):

a) What is the probability that random guessing will lead to a passing (70% or higher) score?


b) Imagine that the Agency decided that 50 questions was too difficult and shortened the test to just 25 questions. To balance this out, they also changed the questions so they each have four options (A, B, C, and D), but still only one possible correct answer. What is the probability that random guessing will lead to a perfect score?



c) Based on the results, do you think the first or second version of the test is safer against examinees guessing to achieve a passing score? Explain your answer.