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In response to a student question: typed/printed work is also acceptable(!), as well as the formats listed below.
Note:Don't worry if the last problem here, KK3.7, doesn't look do-able given what you know now. It will be, by the time we've done next Wednesday's lecture, and so you'll have a whole week to apply your new knowledge to that problem.
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Problem 3: Russian Roulette
In the game of Russian Roulette (NOT recommended by this professor!!),
a player inserts a single bullet into the drum of the revolver,
leaving the other five chambers empty. The player then spins the drum,
points the gun at their head, and pulls the trigger.
(a) What is the probability of being still alive after playing the
game N times?
(b) What is the probability of surviving (N-1) turns in this game
and then being shot the N-th time the trigger is pulled?
(c) What is the average number of times a player gets the opportunity
to pull the trigger in this macabre game?
Problem 4: Two drunks
Two drunks start out together at the origin of the x axis, each having
equal probability of making a step to the left or right along x.
Find the probability that they meet again after N steps. Note
that the drunks take their steps simultaneously.
(Hint: it may help to consider their relative motion)