Probability Problem?

Question

Mr. X, Mr. Y, and Mr. Z are to fight in a three-cornered pistol duel. It is known that Mr. X's chance of hitting his target is 0.3, Mr. Y's is 0.5, and Mr. Z never misses. They are to fire at their choice of target in succession in the order Mr X(0.3 chance), Mr Z(never misses), and Mr Y(0.5 chance). A hit individual is considered dead and no longer shot at, and this duel lasts until one person is left. What should Mr X's strategy be? (If he wants to win).

I've been thinking about this one, and the only possible conclusion I can come up with is try to shoot Mr Z, but then there's a chance you might end up in a never-ending pistol duel between Mr X and Mr Y.

Answer 1

Mr. X must shoot at Mr. Z. If he shoots at Mr Y and hits he can not win as Mr. Z's only shot would be at Mr X, and he never misses.
If Mr. X shoots at Mr Y, and misses (the most likely case), Mr Z can shoot at either Mr. X or Mr. Y. If Mr. Z is logical, he would also shoot at Mr. Y as Mr. Y is a better shot than Mr X. Since he is sure to hit Mr. Y, then Mr. X gets another shot at Mr Z before certain death.

Answer 2

On his first shot Mr. X must deliberately miss.
Then Mr. Z shoots and kills Mr. Y.
Now Mr. X shoots at Mr. Z. He has a 30% chance of surviving and Mr. Z has a 70% chance.

All other options yield inferior chances for Mr. X's survival.

If Mr. X shoots at Mr. Z and hits him, then he has a duel with Mr. Y where Mr. Y shoots first. In this scenario Mr. X's chance of survival is 3/13 ≈ 23.1%.

Answer 3

i elect the ten undesirable--SO i theory this one outONEOUT AND MY answer IS.........27% danger OF GETTIN THE ALL HEARTS IN series FROM AN ACE to 10. it truly is HOW I ARRIVED at my decision, ok???? listen properly reason i in basic terms madeit to indicate 3 after too lengthy of a time and now i'm attempting element 4. if i had fifty 2 playing cards that are in a deck of playing cards and u dealt me 5 like u stated u did--that would go away me with 40 seven playing cards. minus a 10 might want to equivalent 37percentand the percentages on that are even worse-r than that so upload yet another or sub-music yet another 10 for the percentages bein antagonistic to me and that i in basic terms ended up with a 27% and am i ceremony or rong??? i'm a kia

Answer 4

♠ x must skip his first shot somehow; looking at y, x may declare he does want to shed blood and shoots in the air;
♦ now z shoots at y coz y is more dangerous for z; now y being dead, x has 0.3 chance to survive;
♥ unless x skips his move, and really shoots at z and misses; he becomes more dangerous for z coz x’s chance to hit the aim is 0.3+0.3 now; here x will be shot for sure by z!
♥ if x shoots at z and kills him, x’s chance to survive will be 0.3*0.5 only!