SOLUTION: A sample of 4 diffrent calculators is randomly selected from a group containing 18 that are defective and 39 that have no defects. What is the probability that at least one of the
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Question 358945: A sample of 4 diffrent calculators is randomly selected from a group containing 18 that are defective and 39 that have no defects. What is the probability that at least one of the calculators is defective? Answer by solver91311(24713) (Show Source):
The probability of successes in trials where is the probability of success on any given trial is given by:
Where is the number of combinations of things taken at a time and is calculated by
The probability of at least one is the probability of exactly one plus the probability of exactly two plus the probability of exactly three plus the probability of exactly four.
But since that sum plus the probability of exactly zero occurrences equals one, we can calculate the sum by subtracting the probability of exactly zero from 1:
But since and , the above reduces to:
You can do the rest of the arithmetic.
John
My calculator said it, I believe it, that settles it
