PLEASE HELP ME I DONT KNOW HOW TO DO IT Problem 1 Truel A tr

PLEASE HELP ME.. I DON\'T KNOW HOW TO DO IT.

Problem 1. Truel A truel is like a duel except there are three players involved. We will call them player A, player B, and Player C. Each player comes with his probability of hitting a target. Player A hits a target with probability p,-0.9, Player B with probability Pr=0.7 and Player C with probability pc-0.25. The game is played by rounds. At each round the players shoot at each other simultaneously, hence their speed doesn\'t ONLY ONE player is still alive or if all three of them are dead. We assumed that each player has infinitely many bullets. Partl (10 points) (a) Compute the probabilities of winning for each player. (b) Compute the probability that nobody wins. (c) Who is the most likely player to win? Part 2 (10 points) Repeat Part 1 but for the general probabilities, i.e., assume that Player A hits a target with probability pA, Player B with probability pB and Player C with probability Rc Assume in addition that Pa

Solution

I will help you with the first question

a) for winning the player needs to hitting the others players (2)

player A ------0.9/2= 0.45

player B-----0.7/2 = 0.35

player C-----0.25/2 = 0.125

b)

nobody wins that means that all players fails

1-0.9 = 0.1 /2 = 0.05

1-0.7= 0.3/2 = 0.15

1- 0.25 = 0.75/2 = 0.375

0.05+0.15+0.375 = 0.575

c)

the most likely player to win this is player A because he can hits the target with a probability more higher than the other 2 players