Assume that the probability that an airplane engine will...

Assume that the probability that an airplane engine will fail during a torture test is $\frac{1}{2}$ and that the aircraft in question has 4 engines.
Find the probability that exactly 1 engine will survive.

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Key Concepts

Independent Events

In probability theory, independent events are those whose outcomes do not influence each other. This concept is crucial when analyzing multiple random events, such as the performance of several airplane engines, where the failure or survival of one engine does not affect the probability of another engine failing or surviving.

Bernoulli Trials

A Bernoulli trial is an experiment with exactly two possible outcomes: success or failure. Each engine's test can be modeled as a Bernoulli trial, where each engine has a fixed probability (1/2) of surviving (success) or failing (failure), and each trial is independent of others.

Binomial Distribution

The binomial distribution describes the probability of achieving a fixed number of successes in a specific number of independent Bernoulli trials. In this context, it is used to compute the probability that exactly one out of four engines survives, by combining the individual probabilities of success and failure with the various possible arrangements.

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