SOLUTION: Please help me with this problem, I'm stuck on it.
An archer hits his target 60% of the time. If he shoots eight arrows, what is the probability of each event? (Round your answer
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Question 1007598: Please help me with this problem, I'm stuck on it.
An archer hits his target 60% of the time. If he shoots eight arrows, what is the probability of each event? (Round your answers to six decimal places.)
a) He never hits the target.
(b) He hits the target each time.
(c) He hits the target more than once.
(d) He hits the target at least six times.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The probability of 
successes in 
trials where 
is the probability of success on any given trial is given by:
\ =\ {{n}\choose{k}}\left(p\right)^k\left(1\,-\,p\right)^{n\,-\,k})
Where 
is the number of combinations of things taken at a time and is calculated by !})
(a) \ =\ {{8}\choose{0}}\left(0.6\right)^0\left(1\,-\,0.6\right)^{8\,-\,0})
(b) \ =\ {{8}\choose{8}}\left(0.6\right)^8\left(1\,-\,0.6\right)^{8\,-\,8})
(c) \ =\ 1\ -\ \sum_{k=0}^1\,{{8}\choose{k}}\left(0.6\right)^k\left(1\,-\,0.6\right)^{8\,-\,k})
(d) \ =\ \sum_{k=6}^8\,{{8}\choose{k}}\left(0.6\right)^k\left(1\,-\,0.6\right)^{8\,-\,k})
You can do your own arithmetic. Hints: 
. And 
John
My calculator said it, I believe it, that settles it
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