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 5minute 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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 Spring '08
 Staff
 Probability, Probability theory, probability density function, Dice

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