Cornered Duel Probability pls help

Question

A, B, C, D were given pistols for a competition. The participants will try to shoot their competitors. If the person is hit, that person will be out of the competition. The shooting will turn in alphabetical order and will repeat once all have attempted a shot. The participants will take other participants at a higher rate. A has a hit rate of 0.3, B has a hit rate of 1, C has a hit rate of 0.5, and D has a hit rate of 0.7. What is A's winning probability?

Answer 1

This is actually easier to calculate than it looks like at first.

I will assume the participants are given PAINT guns and are properly dressed with safety gear and are at proscribed safe distances. Violence and or killing , even in hypothetical situations is not to be condoned or even considered. This is a violence free site.

For A to win all competitors have to be eliminated (hit by a paint ball) . There are several probability branches that lead to this.

1) A hits B (round1) , A hits C (round2), A hits D (round3) after C misses D in round 1, and D misses A in round 1 and 2

2) A hits B (round1) , A hits C (round2) after C hits D in round 1

3) A misses B (round1), A hits B (round 2) , A hits D ( round 3) after D misses A in round 1 and 2

4) A misses B (round1), A misses B (round 2) , A hits B (round3) after D misses A in round 1

p(1) = .3 *( .3*(1-.7))*(.3*(1-.7)*(1-.5)) : .00125

p(2) = .3*(.3*.5). : .045

p(3) = .7 * (.7 *(1-.7))*(.3*(1-.7)). : .01323

p(4) = .7*(.7*.3)*.3. : .0441

Total chances to win = .10358