An oil prospector will drill a succession of holes in a given area until he finds productive wells. The probability that he is successful on a given trial is 0.3. The prospector can only afford to drill 6 wells.

What is the probability the inspector fails to Önd r productive wells?

0.117649

Step-by-step explanation:

The probability that the prospectors will not find a productive oil.

This is a binomial distribution problem

Binomial distribution function is represented by

P (X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 6 oil wells available to be dug

x = Number of successes required = 0

p = probability of success = 0.3

q = probability of failure = 1 - p = 0.7

P (X = 0) = ⁶C₀ 0.3⁰ 0.7⁶⁻⁰ = (1) (1) (0.7⁶) = 0.117649