# Two Probability Questions

6) One must select from a set of 12 components that are known to contain 4 faulty components. The selection is made at random so that a selection of any component is equally likely.

a) What is the probability of drawing exactly 1 faulty component if 3 different components are drawn?

b) What is the probability of drawing at exactly 2 faulty components if 3 different components are drawn?

5) A rotary switch may take one of five positions in response to voltage inputs. As a system safety designer you have the option of designing the system so that the switch must take two random settings during a mission or only one. However, if you must design for two settings only one position of the switch will be unsafe. If you design for one setting, two positions will be unsafe.

Which is the preferred design?

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#### Solution Preview

6) One must select from a set of 12 components that are known to contain 4 faulty components. The selection is made at random so that a selection of any component is equally likely.

This is an example of a binomial experiment. The general equation for finding the binomial probability is:

We're going to define a success as choosing a faulty component. The probability of success is 4/12, or 0.333.

a) What is the probability of drawing exactly 1 faulty component if 3 different components are drawn?

P(1 success out of 3 trials) = (3 ...