The probability that a lab specimen contains high levels of...

The probability that a lab specimen contains high levels of contamination is $0.10 .$ Five samples are checked, and the samples are independent. (a) What is the probability that none contain high levels of contamination? (b) What is the probability that exactly one contains high levels of contamination? (c) What is the probability that at least one contains high levels of contamination?

The probability that a lab specimen contains high levels of contamination is $0.10 .$ Five samples are checked, and the samples are independent.
(a) What is the probability that none contain high levels of contamination?
(b) What is the probability that exactly one contains high levels of contamination?
(c) What is the probability that at least one contains high levels of contamination?

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Key Concepts

Binomial Distribution

The binomial distribution models the probability of obtaining a fixed number of successful outcomes in a specified number of independent trials, where each trial has the same probability of success. It is used in scenarios where there are exactly two possible outcomes (success or failure) in each trial.

Bernoulli Trials

Bernoulli trials refer to repeated experiments where each experiment has exactly two possible outcomes, often labeled as success and failure. The trials are independent, and the probability of success remains constant from one trial to the next.

Independent Events

Independence means that the outcome of one trial does not affect the outcomes of any other trials. In probability, when events are independent, the probability of a sequence of events occurring is the product of their individual probabilities.

Complement Rule

The complement rule in probability is used to determine the probability that an event does not occur by subtracting the probability that it does occur from one. It is particularly useful when calculating probabilities of 'at least one' occurrences.

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