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# Statistical Analysis of Damaged Components

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Please provide detailed answers and easy to understand explanations for questions below. I have low level background in stats. Any internet references would be helpful for my understanding.

A box contains 10 components of which 4 are damaged. You select 3 components from
the box, one at a time without replacement (that is, you do not return them to the box).
(a) Determine the sample space for the experiment.
(b) Is this a binomial experiment? why or why not?
(c) Draw the probability tree for the experiment.
(d) What is the probability that the last component drawn (the third one) is a damaged one?
(e) Given that the last component drawn (the third one) is a damaged one, what is the probability
that the second drawn component is not damaged?

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#### Solution Preview

See the attached file. Thanks

a) The sample for the experiment is the set of all possible outcomes. Let D denotes a defective component and C denotes a good component, then all possible outcomes for the experiment are:
{DDD, DDC, DCD, DCC, CDD, CDC, CCD, CCC}

b) The main property of a binomial experiment is that the probability of success / failure remains constant across a large number of repetitions. This ...

#### Solution Summary

This solution shows step-by-step calculations and justifications to determine the sample of the experiment, property of the binomial experiment, and probabilities of different scenarios.

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