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Propability Questions

  • #1
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Homework Statement


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?


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:

Answers and Replies

  • #2
statdad
Homework Helper
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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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