Probability Question

[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)

[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.

[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?

[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.

[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

[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

[BicycleTree]

Confirmed, snoble.

[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?

[Moo Of Doom]

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

[BicycleTree]

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