Question

The probability that a man will hit a target is
2 / 3.
If he shoots at the target until he hits it for the first time, find the probability that it will take him 5 shots to hit the target

Answer 1

@Directrix @jim_thompson5910

Answer 2

this one is a hard one

Answer 3

This is basically asking the question of "what is the probability that he will hit the target on the 6th try"

This is assuming that once he hits the target, he can no longer shoot it

Answer 4

So you would use the geometric distribution to answer this question

Answer 5

which means you use this formula

P(X = k) = (1-p)^(k-1)*p

where

p = probability of success of each individual and independent trial
k = trial number where the first success is encountered

Answer 6

i know the book says its 2 / 243, but i dont know process

Answer 7

you just plug in p = 2/3 and k = 6

evaluate and simplify

Answer 8

got it. thmks

Answer 9

oh wait, k = 5, not 6

but everything else is still the same