Respuesta :
Answer:
4.92% probability that the third strike comes on the seventh well drilled
Step-by-step explanation:
For each drill, there are only two possible outcomes. Either it is a strike, or it is not. Each drill is independent of other drills. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
20% chance of striking oil.
This means that [tex]p = 0.2[/tex]
What is that probability that the third strike comes on the seventh well drilled
2 stikers during the first 6 drills(P(X = 2) when n = 6)[/tex]
Strike during the 7th drill, with 0.2 probability. So
[tex]P = 0.2P(X = 2)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{6,2}.(0.2)^{2}.(0.8)^{4} = 0.2458[/tex]
Then
[tex]P = 0.2P(X = 2) = 0.2*0.2458 = 0.0492[/tex]
4.92% probability that the third strike comes on the seventh well drilled
