In a sample of 800 U. S. adults, 171 dine out at a resaurant more than once per week. 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. Required:
a. Find the probability that both adults dine out more than once per week.
b. Find the probability that neither adult dines out more than once per week.
c. Find the probability that at least one of the two adults dines out more than once per week.
d. Which of the events can be considered unusual? Explain.

a) 4.55% probability that both adults dine out more than once per week.

b) 61.80% probability that neither adult dines out more than once per week.

c) 38.20% probability that at least one of the two adults dines out more than once per week.

d) An event is considered unusual if it has a less than 5% probability of happening. Following this rule, in this problem, both adults dining out more than once per week can be considered unusual.

Step-by-step explanation:

The adults are selected without replacement, so we use the hypergeometric distribution to solve this question.

Hypergeometric distribution:

The probability of x sucesses is given by the following formula:

In which:

x is the number of sucesses.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

Combinations formula:

is the number of different combinations of x objects from a set of n elements, given by the following formula.

In this question:

800 adults, so

171 dine out at a resaurant more than once per week, so

2 are chosen, so

a. Find the probability that both adults dine out more than once per week.

This is P(X = 2).

4.55% probability that both adults dine out more than once per week.

b. Find the probability that neither adult dines out more than once per week.

This is P(X = 0).

61.80% probability that neither adult dines out more than once per week.

c. Find the probability that at least one of the two adults dines out more than once per week.

Either none dines out more than once per week, or at least one does. The sum of the probabilities of these events is 100%. So

p + 61.80 = 100

p = 38.20

38.20% probability that at least one of the two adults dines out more than once per week.

d. Which of the events can be considered unusual? Explain.

An event is considered unusual if it has a less than 5% probability of happening. Following this rule, in this problem, both adults dining out more than once per week can be considered unusual.

by definition, an arc subtended by a central angle of some given measure has the same measure. so .

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.