Probability Question

1. May 26, 2005

himurakenshin

Three women A,b,c are involved in a contest with the following rules. A shoots B, if B survives, B shoots C and if C survives, C shoots A. A is 25% accurate, B is 45% and C is 75%. Who is most likely to win if the women continue to shoot in order and in turn. (Who is most likely to be alive)

2. May 26, 2005

BicycleTree

First find the probability that A kills B when there are still 3. This will be .25 (first shot) + .75 * .55 * .25 * .25 (second shot: you get this because for A killing B on second shot with still 3 people, A must miss first shot, then B must miss first shot, then C must miss first shot, then A must hit second shot) + .75 * .55 * .25 * .75 * .55 * .25 * .25 (third shot) + ..., basically the sum of a geometric sequence.

Then find the probability of each player winning given A just killed B.

Continue in this fashion for B killing C and for C killing A and deal with the conditional probabilities appropriately.

3. May 27, 2005

mathman

The statement of the problem has a gap. What happens after one person is killed? Who shoots next? Do they take turns? Is the killing prob. the same?

4. May 27, 2005

BicycleTree

It's probably assumed that they go in order, so if someone just shot and killed then the other surviving person shoots next. The hit probabilities are stated.

5. May 27, 2005

himurakenshin

When I solved the answer, I find that B has the highest probability of winning, can anyone verify this.

Also once on person is dead they shoot each other

6. May 27, 2005

snoble

I may be wrong but my estimates are that C has a 42% chance of winning, B has a 40% chance of winning and A has a 18% chance of winning. Though I did that very quickly so I could have easily made a mistake.

Steven

7. May 27, 2005

BicycleTree

Confirmed, snoble.

8. May 28, 2005

himurakenshin

this is the workings as how I got the answer that B has the highest probability - can somebody tell me where I have gone wrong?

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9. May 28, 2005

Moo Of Doom

One thing I can tell you is that your probabilities add up to 110.6%, which just can't be right...

10. May 28, 2005

BicycleTree

Under B, where A dies first, you must have punched in the numbers wrong.

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