**MATH 425-4: EXTRA CREDIT PROBLEMS III**

Math 425-4, Fall 1997

Prof. Hochster

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** 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]

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