Question 74150: an olymp[ic archer is able to hit the bullseye 80% of the time. assume each shot is independent of the othjers. if she shoots 6 arrows, whats the probability of the result below?
a) the 1st bullseye comes on the 3rd arrow
b)she misses the bullseye at least once
c)the 1st bullseye comes on the 4th or 5th arrow
d)gets exactly 4 bullseyes
e)gets at least 4 bullseyes
f)gets at most 4 bullseyes
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! an olymp[ic archer is able to hit the bullseye 80% of the time. assume each shot is independent of the othjers. if she shoots 6 arrows, whats the probability of the result below?
-----------
P(hit)=0.8
P(miss)=0.2
a) the 1st bullseye comes on the 3rd arrow
He has to miss,miss,hit
P(mmh)=(0.2)^2(0.8) =0.032
-------------------
b)she misses the bullseye at least once
P(at least one hit) = 1 - P(all misses)
= 1 - 0.2^6= 1-(6,4 x 10^-5)= 0.999936....
------------
c)the 1st bullseye comes on the 4th or 5th arrow
These are disjoint events, so:
P(4th or 5th) = 0.2^3*0.8+0.2^4*0.8 = 0.00768
-------------
d)gets exactly 4 bullseyes
This is binomial with n=6,p=.8,x=4
If you have a TI calculator use binompdf(6,0.8,4)=0.24576
----------------
e)gets at least 4 bullseyes
Use [1 - binomcdf(6,0.8,3)]=0.90112...
----------------
f)gets at most 4 bullseyes
Use binomcdf(6,0.8,4)=0.34464
---------
Cheers,
Stan H.
|
|
|
