## MATH 425-4: EXTRA CREDIT PROBLEMS III

Math 425-4, Fall 1997
Prof. Hochster

EC#10. Suppose that your chance of being in a plane crash on a given flight is one in a million. You are a frequent flier and you fly one million times. What is the probability that you will be in at least one crash? (Assume that the flights are independent events.) For full credit you should observe that the answer can be expressed, almost but not exactly, in terms of one of the fundamental constants of mathematics. (Flying a million times is tough - ten thousand flights a year for 100 years will do it, and that means over 27-28 flights a day.) [9/26]

EC#11. You flip a fair coin fifty times. Investigate the following question: what is the probability that at all times during the flipping, there have been at least as many heads as tails? [No deadline yet]

EC#12. Investigate the following problem: how many ways are there to "make sense of" or carry out a sum with n terms by putting in parentheses? You may not change the order of the terms. For three terms there are two ways: (a+b)+c or a+(b+c) and for four terms there are five ways: ((a+b) + c) + d, (a+(b+c))+d, (a+b)+(c+d), a+((b+c)+d), and a+(b+(c+d)). [No deadline yet]