SOLUTION: basic statistics: A box contains 18 transistors of which 3 are defective. If sample three of the transistors, Find the probability that we would find exactly 1 defective transistor
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Question 281995: basic statistics: A box contains 18 transistors of which 3 are defective. If sample three of the transistors, Find the probability that we would find exactly 1 defective transistor. And find the probability that we would find at least 1 defective transistor. Answer by solver91311(24713) (Show Source):
The probability of selecting a defective transistor on a single trial is . The probability of successes in trials where the probability of success on any given trial is is given by:
where is the number of ways to choose things from things and is equal to
For the first part of your problem you need to calculate:
There are two ways to do the second part of your problem:
You can calculate
Which involves considerable drudgery. On the other hand, you could realize that finding at least one is all possibilities EXCEPT finding none, so you could calculate:
