Reliability of a Machine A machine that is used in a manufacturing process has four separate components, each of which has a probability of failing on any given day. If any component fails, the entire machine breaks down. Find the probability that on a given day the indicated event occurs.
(a) The machine breaks down.
(b) The machine does not break down.
(c) Only one component does not fail.
The probability that on a given day machine breaks down.
The number of components is .
The probability of a component failing on any given day is .
Write the expression for the probability of success in a trial.
Here, is the probability of success.
Write the expression to find the probability of failure in a trial.
Here, is probability of failure.
Write the expression to find the probability of getting exactly success in given number of independent trials of the experiment.
Here, is the number of trial and is the number of success in the given experiment.
Write the formula to find the number of combinations.
Substitute for in equation . Then,
The probability that on a given day machine does not break down.
The probability that on a given day only one component does not fail.
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