Respuesta :
Answer:
3.07% probability that the third oil strike comes on the fifth well drilled.
Step-by-step explanation:
For each oil drill, there are only two possible outcomes. Either there is a strike, or there is not. The probability that oil is striken in a trial is independent of other trials. 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.
Strike oil with probability 0.20.
This means that [tex]p = 0.2[/tex]
Find the probability that the third oil strike comes on the fifth well drilled.
2 strikes on the first four drills(P(X = 2) when n = 4) and strike on the fifth(0.2 probability).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 2) = C_{4,2}.(0.2)^{2}.(0.8)^{2} = 0.1536[/tex]
0.2*0.1536 = 0.0307
3.07% probability that the third oil strike comes on the fifth well drilled.
