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4802Probability07 - Math 4802 Fall 2007 Probability...

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Math 4802 Fall 2007 Probability Problems Due Tuesday, September 11: 1. Shuffle an ordinary deck of 52 playing cards, and then turn the cards face up one at a time. On average, how many cards are required to produce the first ace? 2. Show that the probability that December 25 th falls on a Wednesday is not 1 / 7. (Leap years have 366 days; other years have 365 days. Year n is a leap year iff either (a) 4 divides n and 100 does not divide n , or (b) 400 divides n .) 3. Duels in the town of Putnamville are usually not fatal. Each contestant in a duel arrives at a random moment between 6AM and 7AM on the prescribed day, stays for 5 minutes, and then leaves, unless his opponent arrives within that 5-minute interval, in which case they fight to the death. What fraction of duels lead to casualties? 4. A drunken man standing one step from the edge of a cliff takes a se-
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