Question

In a survey of U.S. adults with a sample size of 2021​, 398 said Franklin Roosevelt was the best president since World War II. Two U.S. adults are selected at random from the population of all U.S. adults without replacement. Assuming the sample is representative of all U.S.​ adults, complete parts​ (a) through​ (d).
(a) Find the probability that both adults say Franklin Roosevelt was the best president since World War II.
The probability that both adults say Franklin Roosevelt was the best president since World War II =
​(Round to three decimal places as​ needed.)
​(b) Find the probability that neither adult says Franklin Roosevelt was the best president since World War II.
The probability that neither adult says Franklin Roosevelt was the best president since World War II =
​(Round to three decimal places as​ needed.)
​(c) Find the probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II.
The probability that at least one of the two adults says Franklin Roosevelt was the best president since World War II =
​(Round to three decimal places as​ needed.)
​(d) Which of the events can be considered​ unusual? Explain. Select all that apply:
a.The event in part​ (b) is unusual because its probability is less than or equal to 0.05.
b.None of these events are unusual
c.The event in part​ (c) is unusual because its probability is less than or equal to 0.05.
d. The event in part (a) is unusual because its probability is less than or equal to 0.05.

Answer 1

Answer:

(a)0.039

(b)0.645

(c)0.316

(d)Event in Part (a)

Step-by-step explanation:

Sample size = 2021​

Number who said Franklin Roosevelt was the best president since World War II=398

Note that in a selection without replacement, the total population reduces after each selection.

If two adults are selected at random from the population of all U.S. adults without replacement:

Let X represent those who say Franklin Roosevelt was the best president

Ley Y represent those who disagree

(a)Probability that both adults say Franklin Roosevelt was the best president since World War II

Pr(XX)=$\frac{398}{2021}X \frac{397}{2020}=0.039$

(b)Probability that neither adult says Franklin Roosevelt was the best president

Number of those who disagree=2021-398=1623

Pr(YY)=$\frac{1623}{2021}X \frac{1622}{2020}=0.645$

(c)Probability that at least one of the two adults says Franklin Roosevelt was the best president

Pr(XY) or Pr(YX)=$(\frac{398}{2021}X \frac{1623}{2020})+(\frac{1623}{2021}X \frac{398}{2020})$=0.316

(d)The event in part (a) is unusual because its probability is less than or equal to 0.05.