An electronic product contains 40 integrated circuits. The...

An electronic product contains 40 integrated circuits. The probability that any integrated circuit is defective is $0.01,$ and the integrated circuits are independent. The product operates only if there are no defective integrated circuits. What is the probability that the product operates?

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Key Concepts

Independent Events

In probability, independent events are those whose outcomes do not affect one another. This means the probability of a combination of independent events occurring together is the product of their individual probabilities.

Multiplication Rule

The multiplication rule states that if events are independent, then the probability of all events happening is the product of the probabilities of each individual event. This rule is fundamental when calculating the overall probability of multiple independent events occurring.

Bernoulli Trials and the Binomial Distribution

A Bernoulli trial is a random experiment with exactly two possible outcomes (commonly termed success and failure) and a constant probability of success. When such experiments are repeated independently a fixed number of times, the total number of successes follows a Binomial Distribution. Calculating the probability of zero successes (or zero failures) in this context is a direct application of the binomial probability formula.

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