Question

the pie chart to the right shows how adults rate their financial shape. suppose 20 people are chosen at random from a group of 400. what is the probability that none of the 20 people would rate their financial shape as fair? (make the assumption that the 400 people are represented by the pie chart.)

the probability that none of the 20 people would rate their financial shape as fair is 0.000046.
(round to six decimal places as needed.)

Explanation:

Identify the population parameters

Using the Sampling Without Replacement and Combinatorics knowledge points

$$
LATEXBLOCK0
$$

Set up the hypergeometric probability

Using the Hypergeometric Distribution knowledge point

$$ P(X = 0) = \frac{\binom{248}{20} \binom{152}{0}}{\binom{400}{20}} = \frac{\binom{248}{20}}{\binom{400}{20}} $$

Calculate the combination terms

Using the Combinatorics knowledge point

$$
LATEXBLOCK1
$$

Compute the product and round

Using the Hypergeometric Distribution knowledge point

$$
LATEXBLOCK2
$$

Answer:

The pie chart to the right shows how adults rate their financial shape. Suppose 20 people are chosen at random from a group of 400. What is the probability that none of the 20 people would rate their financial shape as fair? (Make the assumption that the 400 people are represented by the pie chart.)

The probability that none of the 20 people would rate their financial shape as fair is <blank>0.000037</blank>.
(Round to six decimal places as needed.)