Nutritional Information In a sample of 1000 U.S. adults, 150...

Nutritional Information In a sample of 1000 U.S. adults, 150 said they are very confident in the nutritional information on restaurant menus. Four U.S. adults are selected at random without replacement. (Adapted from Rasmussen Reports) (a) Find the probability that all four adults are very confident in the nutritional information on restaurant menus. (b) Find the probability that none of the four adults are very confident in the nutritional information on restaurant menus. (c) Find the probability that at least one of the four adults is very confident in the nutritional information on restaurant menus. (d) Which of the events can be considered unusual? Explain.

Nutritional Information In a sample of 1000 U.S. adults, 150 said they are very confident in the nutritional information on restaurant menus. Four
U.S. adults are selected at random without replacement. (Adapted from Rasmussen Reports)
(a) Find the probability that all four adults are very confident in the nutritional information on restaurant menus.
(b) Find the probability that none of the four adults are very confident in the nutritional information on restaurant menus.
(c) Find the probability that at least one of the four adults is very confident
in the nutritional information on restaurant menus.
(d) Which of the events can be considered unusual? Explain.

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Key Concepts

Hypergeometric Distribution

This distribution models the probability of obtaining a given number of successes in a sample drawn from a finite population without replacement. It is used when the sample is drawn in a way that the outcome of one pick affects the probabilities of subsequent picks.

Combinatorics

Combinatorial methods, particularly the use of combinations, are essential for counting the number of ways to select items from a set. This is a fundamental tool in calculating probabilities in scenarios where order does not matter and sampling is done without replacement.

Complementary Probability

This concept involves calculating the probability of an event by subtracting the probability of its complement from one. It is particularly useful in cases like finding the probability of 'at least one' occurrence when the direct calculation is more complex.

Identification of Unusual Events

In statistics, an event is often considered unusual if its probability is very low, typically below a certain threshold. Recognizing which events are unusual helps in understanding the significance of outcomes and in making decisions or predictions based on probabilistic models.

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