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Propability Questions

  1. Sep 14, 2013 #1
    1. The problem statement, all variables and given/known data
    1.In the ``game'' of Russian roulette, the player inserts a single cartridge into the drum of a revolver, leaving the other five chambers of the drum empty. The player then spins the drum, aims at his/her head, and pulls the trigger. 1.What is the probability of the player still being alive after playing the game [tex]N[/tex] times?
    2.What is the probability of the player surviving [tex]N-1[/tex] turns in this game, and then being shot the [tex]Nth[/tex] time he/she pulls the trigger?
    3.What is the mean number of times the player gets to pull the trigger?


    3. The attempt at a solution
    (I'm in the process of learning LaTex, but for now....)

    1. The chances of the person still being with 5 chambers is

    [tex]\sum_{n=zero}^4 \frac{1}{5-n}[/tex]
    series from n=0 to n=4 (1/(5-n)
    right? This would equate to 1/(5-0) + 1/(5-1) + 1/(5-2) etc etc...

    i'm a bit stumped at question #2 however.
     
    Last edited: Sep 14, 2013
  2. jcsd
  3. Sep 14, 2013 #2

    statdad

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    Homework Helper

    First write out the chance that when the trigger is pulled the bullet is not under the hammer: this will also give you the chance the bullet is under the hammer.
    Now for the first question: if the player is still alive after N trigger pulls, the bullet was not under the hammer any of those times (not the first AND not the second AND ... AND not the Nth): how would you find the probability of that joint event?

    For the second: if the player is not shot until trigger pull N, that means the first N-1 tries did not have the bullet under the trigger AND the Nth trigger pull did: find the probability of that joint event.

    As a start to see what happens, you might try working out each solution in the very special case N = 3, just to see how the numbers work out.
     
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