Problem 24E

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.

Answer

Step 1 of 4

(a)

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.

We are asked to find the probability that all four adults are very confident in the nutritional information on restaurant menus.

Let denote the event that U.S. adults are very confident in the nutritional information on restaurant menus.

Hence the probability that the U.S. adults are very confident in the nutritional information on restaurant menus is,

Since the individual probability is

Using the independence rule of probability, we can find the probability that all four adults are very confident in the nutritional information on restaurant menus.

Hence the probability is