Question

# 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 0.2. What is the probability that the third hole drilled is the first to yield a productive well?

Probability and combinatorics
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 0.2. What is the probability that the third hole drilled is the first to yield a productive well?

Given: $$p = 0.2$$ $$q = 1 - p = 1 - 0.2 = 0.8$$
Definition geometric probability: $$p(y) = q^{y-1}p$$
Evaluate at y = 3: $$p(3) = 0.8^{3-1} * 0.2 = 0.128 = 12.8\%$$
Result: $$0.128\ or\ 12.8\%$$