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Answer:
3.90% probability that the third failure will occur on the tenth component tested
Step-by-step explanation:
For each component, there are only two possible outcomes. Either it fails, or it does not fail. Components perform independently. 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.
Assume that a component passes a test is 0.85
So they fail with probability of
What is the probability that the third failure will occur on the tenth component tested
First 9 components: Two failures, that is, P(X = 2) when n = 9.
10th component: Failure with probability 0.15.
So
In which
So
3.90% probability that the third failure will occur on the tenth component tested