Final answer:
The probability that the third strike comes on the fifth well drilled is calculated using the geometric distribution. The mean and variance of the number of wells needed to set up three producing wells can be found using the negative binomial distribution.
Step-by-step explanation:
To find the probability that the third strike comes on the fifth well drilled, we can use the geometric distribution. The formula for the geometric distribution is P(X=k)=(1-p)^(k-1)p, where X is the number of trials until the first success, p is the probability of success, and k is the number of trials.
In this case, the probability of striking oil is 25% or 0.25. So, the probability that the third strike comes on the fifth well drilled is (1-0.25)^(5-1)*0.25.
To find the mean and variance of the number of wells that must be drilled to set up three producing wells, we can use the negative binomial distribution. The negative binomial distribution is a generalization of the geometric distribution and is used to model the number of trials until a specified number of successes.
The mean of the negative binomial distribution is given by μ=r/p, and the variance is given by σ^2=r(1-p)/p^2, where r is the number of successes and p is the probability of success.
In this case, we want to set up three producing wells, so r=3 and p=0.25. Therefore, the mean of the number of wells that must be drilled is 3/0.25=12, and the variance is 3(1-0.25)/0.25^2=36.