Only about 20% of exploratory wells drilled in geologically favorable locations yield commercially viable quantities of oil. Suppose four wells are independently drilled in favourable locaions.
What is the probability at least two wells will yield oil?
the answer given in the text book is 0.1808
Set up the binomial distribution with:
n = 4
p = .20
(1-p) = .80
We are trying to find P(X>=2) which is P(2) + P(3) + P(4), or we can take a shortcut and find [1 – (P(0) + P(1)) using the laws of probability.
P(0) = n!/((n-x)!) p^x (1-p)^(n-x)
P(0) = 4×3x2/(4×3x2) (0.2)^0 (0.8)^4 = 0.4096
P(1) = 4×3x2/3×2 (0.2)^1 (0.8)^3 = 0.4096
1 – (0.4096 + 0.4096) = 0.1808
October 22nd, 2009 at 7:04 am
Set up the binomial distribution with:
n = 4
p = .20
(1-p) = .80
We are trying to find P(X>=2) which is P(2) + P(3) + P(4), or we can take a shortcut and find [1 – (P(0) + P(1)) using the laws of probability.
P(0) = n!/((n-x)!) p^x (1-p)^(n-x)
P(0) = 4×3x2/(4×3x2) (0.2)^0 (0.8)^4 = 0.4096
P(1) = 4×3x2/3×2 (0.2)^1 (0.8)^3 = 0.4096
1 – (0.4096 + 0.4096) = 0.1808
References :