Answer to Question #328413 in Statistics and Probability for Subham

Question

In an oil exploration in Arabic sea, suppose that the probability of an oil strike is 1 in 500 drilling. What is the probability of having exactly 1 oil producing well in 800 explorations.

Answer 1

Let p = 1 / 500 = 0.002, n = 800

According to the binomial distribution:

$P(x=k)=C_n^kp^k(1-p)^{n-k}\\ P(x=1)=800p(1-p)^{800-1}=\\=800\cdot0.002\cdot0.998^{799}\approx\\ \approx0.3232=32.32\%$