A recent geological study in western Texas indicates that exploratory oil wells

Question

A recent geological study in western Texas indicates that exploratory oil wells strike with probability 0.20. (i.e., oil is found). (a) Treating each well as a "trial", suppose that drilling wells in this region obeys the three Bernoulli trial assumptions. State what this would imply (i.e., just describe the three assumptions in the background of the problem). (b) What is the probability that the 1st successful well is found on the 2nd well drilled? (c) What is the probability that the 2nd successful well is found on the 4th well drilled? (d) What is the probability that it will take more than 2 wells to first the 1st successful well? Jerry gives Tom a box of 100 pieces of chocolate, in which 5 are made with Carolina Reaper. (a) Tom randomly eats 10 pieces of chocolate, what is the probability that none of them is made with Carolina Reaper? (b) Tom randomly eats 10 pieces of chocolate, what is the probability that at most 2 pieces of chocolates are made with Carolina Reaper? Let Y be the number of calls received per day by the USC Campus Police. Suppose that Y has a Poisson distribution with lambda = 6.5. (a) What is the probability that on a given day there are exactly 5 calls? at least 5 calls? at most 5 calls? (b) What is the mean of Y? Interpret it using the context of the problem.

Explanation / Answer

Solution:-

6)

p = 5/100

p = 0.05

a) Tom randomly eats 10 pieces of chocolate, the probability that none of them is made with Carolina Reaper is 0.5987.

n = 10, x = 0

By applying binomial distribution:-

P(x, n, p) = nCx*p x *(1 - p)(n - x)

P(x = 0) = 0.5987

b) Tom randomly eats 10 pieces of chocolate, the probability that atmost 2 of them is made with Carolina Reaper is 0.9885.

n = 10, x = 2

By applying binomial distribution:-

P(x, n, p) = nCx*p x *(1 - p)(n - x)

P(x < 2) = P(x = 0) + P(x =1) + P(x = 2)

P(x < 2) = 0.9885

Tom randomly eats 10 pieces of chocolate, the probability that atmost 2 of them is made with Carolina Reaper is 0.9885.

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