SOLUTION: NEED HELP with this one, please! Two hunters, A and B, hunt geese by the following way: the geese appear successively, and when one of them appears, both hunters shoot it

Question 868529: NEED HELP with this one, please!

Two hunters, A and B, hunt geese by the following way: the geese appear successively, and when one of them appears, both hunters shoot it at the same time. A achieves to shoot the goose with probability 1/2, and B succeeds to shoot it with probability 1/4. The outcomes of the shots are independent among them. The goose is killed if at least one of the hunters achieves to shoot it, and it survives if both of the hunters miss it. Because the shots are at the same time, if the goose is killed, none of A and B is sure that, indeed, achieved to shoot it.

Questions:

a) From the geese that they appear, which percentage escapes, and what percentage is hit from both hunters?

b) Given that one goose is hit,what is the probability that only A achieved to shoot it?

c) If 100 geese appear on total, what is the probability that exactly 10 geese survive?

d) If 5 geese appear and they have all survived, what is the probability the first goose that will be killed is the 8th?

Use the known types of Bernoulli, or Poisson, or binominal distribution.

For ex.
Found 3 solutions by ewatrrr, richwmiller, ScientificArt:
Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!

Hi
My thoughts;
Ap = 1/2, Bp = 1/4 P(Hit) = 3/4 0r 75%
The outcomes of the shots are independent among them
a) 25% escape, 75% hit by the hunters
b)P(A|hit) = .5/.75
c) n= 100, P(x=10survive) = bionom(100, .25, 10)
d) If 5 gooses appear and they have all survived, then, Use n = 3
P(8th is hit) = P(x>2) =1- binomcdf(3,.75, 2)
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
No such thing as "gooses"!
We say "geese" in English!
Answer by ScientificArt(6)   (Show Source): You can put this solution on YOUR website!
� Great and completely justified answer from the most helpful tutor so far,ewatrr.
I would solve it exactly the same way like she did.
� I would like to apologise, though, in advance for the most common uneducated troll and completely unrelated with math, richwmiller!
This moron even changed your initial question. Sorry about that too.
You all need to understand that richwmiller has braindamage or something like that. :)

Good luck with your homework, student! Don't hesitate to post further math questions in the future!
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