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Refer to Exercise 3.70. The prospector drills holes until
Chapter 3, Problem 82E(choose chapter or problem)
Problem 82E
Refer to Exercise 3.70. The prospector drills holes until he finds a productive well. How many holes would the prospector expect to drill? Interpret your answer intuitively.
An oil prospector will drill a succession of holes in a given area to find a productive well. The probability that he is successful on a given trial is .2.
a What is the probability that the third hole drilled is the first to yield a productive well?
b If the prospector can afford to drill at most ten wells, what is the probability that he will fail to find a productive well?
Questions & Answers
QUESTION:
Problem 82E
Refer to Exercise 3.70. The prospector drills holes until he finds a productive well. How many holes would the prospector expect to drill? Interpret your answer intuitively.
An oil prospector will drill a succession of holes in a given area to find a productive well. The probability that he is successful on a given trial is .2.
a What is the probability that the third hole drilled is the first to yield a productive well?
b If the prospector can afford to drill at most ten wells, what is the probability that he will fail to find a productive well?
ANSWER:
Solution:
Step 1 of 3:
Given, the probability that he is successful on a given trial is 0.2.
Let Y be the number of holes drilled until the first productive well is found.
Here Y has a geometric distribution with
The probability mass function of geometric distribution is
Here p = 0.20, q = 1- p
= 1- 0.20
= 0.80.
Then,