The Environmental Protection Agency (EPA) has contracted with your company for equipment to monitor water quality for several la
1 answer:
Answer:
36.58% probability that one of the devices fail
Step-by-step explanation:
For each device, there are only two possible outcomes. Either it fails, or it does not fail. The probability of a device failling is independent of other devices. 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.
A total of 15 devices will be used.
This means that
Assume that each device has a probability of 0.05 of failure during the course of the monitoring period.
This means that
What is the probability that one of the devices fail?
This is
36.58% probability that one of the devices fail
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and so the series converges.
You also could have used the fact that the series is geometric with common ratio less than 1 to arrive at the same conclusion, with the added perk of being able to find the exact value of the sum to corroborate this.