Math 4802Fall 2007Probability ProblemsDue Tuesday, September 11:1.Shuffle an ordinary deck of 52 playing cards, and then turn the cards faceup one at a time. On average, how many cards are required to producethe first ace?2.Show that the probability that December 25thfalls on a Wednesday isnot 1/7. (Leap years have 366 days; other years have 365 days. Yearnis a leap year iff either (a) 4 dividesnand 100 does not dividen, or (b)400 dividesn.)3.Duels in the town of Putnamville are usually not fatal. Each contestantin a duel arrives at a random moment between 6AM and 7AM on theprescribed day, stays for 5 minutes, and then leaves, unless his opponentarrives within that 5-minute interval, in which case they fight to thedeath. 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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