Question 999827: 1. Jed Clampett, the president of Ozark Oil, plans to conduct a preliminary survey to locate oil deposits. The probability of striking oil at a single location is 0.15, independent of all other locations.
(a) If Jed decides to drill for oil at 20 different locations, what is the probability that he will strike oil at 3 or more of those locations?
(b) If Jed decides to drill for oil at 200 locations, approximate the probability that he will strike oil at 30 or more of these locations. Justify any approximation procedure that you use.
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 !})
For part a, you need the probability of exactly 3, plus the probability of 4, plus...up to 20.
\ =\ \sum_{k=3}^{20}\, {{20}\choose{k}}\left(0.15\right)^k\left(0.85\right)^{20\,-\,k})
Which is the same as 1 minus the sum of the probabilities of 0, 1, and 2 out of 20 trials:
\ =\ 1\ -\ \sum_{k=0}^{2}\, {{20}\choose{k}}\left(0.15\right)^k\left(0.85\right)^{20\,-\,k})
and involves one hell of a lot less arithmetic.
for part b:
1 minus the sum of the probabilities of 0 through 29 of 200 trials:
\ =\ 1\ -\ \sum_{k=0}^{29}\, {{200}\choose{k}}\left(0.15\right)^k\left(0.85\right)^{200\,-\,k})
Which is way too much ugly arithmetic for me. Use Excel on a PC or Numbers on a Mac
=1 - BINOMDIST(29,200,0.15,TRUE)
John
My calculator said it, I believe it, that settles it
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