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\item[A]
{\bf Modified birthday paradox} There are $n$ people in a room. They
start calling out their birthdays in (some) order. If anybody else's
birthday matches then person says STOP and the game stops, else the
person who called out his/her birthday leaves the room. What is the
probability that at least $k$ people leave the room given that the $n$
people were chosen randomly to start with.

\item[B]
Consider a drunkard who starts at the bottom of a flight of stairs
(step 0) and at each step either takes one step up or skips a step and
takes two steps up. He does either with equal probability. Calculate
the probability $p_k$ that he doesn't skip step $k$.  

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