MATH 431 Midterm: 2011 Math 431 - Seppalainen - Spring Exam 2
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431 introduction to the theory of probability spring 2011. The point total is 100: 1000 people each ip a fair coin 400 times. An eccentric millionaire promises a prize for every person who gets at least 230 heads. Let a be the event that nobody wins a prize. In parts (b) and (c) below explain precisely the approximations you use. (a) (20 pts) give the exact mathematical formula for the probability. P (a). (this is a formula that you could give to a computer but clearly too complicated for hand calculation. ) (b) (30 pts) find a simple decimal estimate for the probability that 400. Ips of a fair coin give at least 230 heads. (c) (10 pts) find a simple good estimate for the probability p (a). The answer is a simple mathematical expression, but not a decimal number since calculators are not used: (a) (10 pts) let x have uniform distribution between 1 and 3.
