Answer:
a) 18.77% probability that the driller drills at 10 locations and has 1 success
b) 75.60% probability that the driller drills at 10 locations and has at least 2 success
Step-by-step explanation:
For each drill, there are only two possible outcomes. Either it is a success, or it is not. The probability of a drill being a success is independent of other drills. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
10 locations
This means that
Suppose the probability of a success at any specific location is 0.25.
This means that
(a) What is the probability that the driller drills at 10 locations and has 1 success?
This is P(X = 1).
18.77% probability that the driller drills at 10 locations and has 1 success
(b) What is the probability that the driller drills at 10 locations and has at least 2 success?
Either there are less than 2 success, or there are at least 2. The sum of the probabilities of these events is decimal 1. So
We want
So
In which
75.60% probability that the driller drills at 10 locations and has at least 2 success