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 200. what is the probability that none of the 20 people would rate their financial shape as fair? (make the assumption that the 200 people are represented by the pie chart.)

excellent 6%
good 42%
fair 37%
poor 13%
other 2%

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

Explanation:

Determine the population counts

Using the Hypergeometric Distribution and Combinatorics knowledge points

$$
LATEXBLOCK0
$$

Set up the probability ratio

Using the Hypergeometric Distribution and Combinatorics knowledge points

$$
LATEXBLOCK1
$$

Calculate the combination values

Using the Combinatorics knowledge point

$$
LATEXBLOCK2
$$

Compute the final decimal value

Using the Hypergeometric Distribution knowledge point

$$
LATEXBLOCK3
$$

Answer:

The probability that none of the 20 people would rate their financial shape as fair is <blank>0.000091</blank>.