A town has 2 fire engines operating independently. The...

A town has 2 fire engines operating independently. The probability that a specific engine is available when needed is 0.96 .
(a) What is the probability that neither is available when needed?
(b) What is the probability that a fire: engine is available when needed?

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Key Concepts

Addition Rule for Unions

The addition rule for unions is used to calculate the probability that at least one of multiple events occurs. For independent events, once the probability of none occurring is known (often using complementary probability), the probability of at least one occurring is simply one minus the probability that none occur. This rule is vital when evaluating scenarios with multiple potential sources of success.

Independent Events

Independent events are events where the occurrence of one does not affect the occurrence of the other. In probability theory, this means that the probability of both events occurring is the product of their individual probabilities. This concept is essential for solving problems where multiple, unrelated events occur simultaneously.

Complementary Probability

Complementary probability refers to the probability that an event does not occur, calculated by subtracting the probability of the event occurring from one. This idea is useful when determining the likelihood of the non-occurrence of an event, such as finding the probability that neither of two independent engines is available.

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