### Write the frequency distribution table for this problem.

Question 1: In a sample of 500 families, 90 have a yearly income of less than \$50,000, 180 have a yearly income of \$50,000 to \$ 100,000, and the remaining families have a yearly income of more than \$100,000.

Write the frequency distribution table for this problem. Calculate the relative frequencies for all classes.
Income Frequency Relative Frequency
Less than \$50,000 \$ 50,000to \$ 100,000 More than \$ 100,000

a. Suppose one family is randomly selected from these 500 families. Find the probability that this family has a yearly income of less than \$50,000.
P (Income is less than \$50,000) =

b. Suppose one family is randomly selected from these 500 families. Find the probability that this family has a yearly income of more than 100,000.
P (Income is more than \$100,00) =

Question 2:

A ski patrol unit has five members available for duty, and two of them are to be sent to rescue an injured skier. In how many ways can two of these five members be selected?

Now suppose the order of selection is important. How many arrangements are possible in this case?

Question 3:

A small ice cream shop has 14 flavors of ice cream and 4 kinds of toppings for its sundaes. How many different selections of one flavor of ice cream and one kind of topping are possible?

Total selections
exact number, no tolerance

Question 4:

How many different outcomes are possible for 5 roils of a die? Number of outcomes

Question 5:

Six hundred adults were asked whether or not they watch for calories and fat content when they buy groceries. The following table gives the two-way classification of their responses, where yes means that an adult watches for calories and fat content and no means he/she does not watch.

 Yes No No Opinion Men 71 171 58 Women 103 129 68

If one adult is randomly selected from these 600 adults, find the following probabilities. Give exact answers in fraction form.
a. P(man or no) =
b. P(yes or woman) =
c. P(no opinion or yes) =

Question 6:

Given that A and B are two mutually exclusive events, find P(A or 8) for the following. a. P(A) = 0.66 and P(B) = 0.08
PO or 8) =
b PO) = 0.45 and K(B) = 0.35
PO or 8) =

Question 7:

The probability that a student graduating from Suburban State University has student loans to pay off after graduation is 0.80. If two students are randomly selected from this university, what is the probability that neither of them has student loans to pay off after graduation?

Enter the exact answer.
P(neither student selected has loans to pay off)= exact number, no tolerance

Question 8:

In a statistics class of 44 students, 12 have volunteered for community service in the past. If two students are selected at random from this class, what is the probability that both of them have volunteered for community service?

Round your answer to four decimal places.

P(both students have volunteered for community service)= the absolute tolerance is +/-0.0005

Question 9:

Given that P(B) = 0.36 and P(A and B) = 0.33 find to 3 decimal places P(A | B).
P(A|B)
the absolute tolerance is +1-0.001

Question 10:

find the joint probability of A and B for the following.
PO) = 0.56 and P(BIA) = 0.85
Enter the exact answer.
PO and B) =
exact number, no tolerance

Question 11:

Find the joint probability of A and B for the following.
P(A) = 0.51 and P(BIA) = 0.65
Enter the exact answer.
P(A and B) =
exact number, no tolerance

Question 12:

In a survey, 500 randomly selected adults who drink coffee were asked whether they usually drink coffee with or without sugar. Of these 500 adults, 310 are men and 200 drink coffee without sugar. Of the 200 who drink coffee without sugar, 140 are men. Are the events man and drinking coffee without sugar independent?

Question 13:

2023 randomly selected adults were asked whether or not they have ever shopped on the Internet. The following table gives a two-way classification of the responses.
Have Shopped Have Never Shopped
Male 500 700
Femalel 300 523

Round your answers to three decimal places.
If one adult is selected at random from these 2023 adults, find the probability that this adult
i. has never shopped on the Internet.
ii. is a male.
iii. has shopped on the Internet given that this adult is a female.
iv. is a male given that this adult has never shopped on the Internet.

Question 14:

In a sample of 500 families, 80 have a yearly income of less than \$40,000, 2.10 have a yearly income of \$40,000 to \$80,000, and the remaining families have a yearly income of more than \$ 80,000.

Write the frequency distribution table for this problem. Calculate the relative frequencies for all classes.
Income Frequency Relative Frequency
Less than \$40,000 \$ 40,000to \$ 80,000 More than \$80_000

a. Suppose one family is randomly selected from these 500 families. Find the probability that this family has a yearly income of less than \$40,000. P(income is less than \$40,000

b. Suppose one family is randomly selected from these 500 families. Find the probability that this family has a yearly income of more than \$80.000. P(income is more than \$ 80,000) =

Question 15:

A hat contains 33 marbles. Of them, 8 are red and 25 are green. If one marble is randomly selected out of this hat, what is the probability that this marble is green?
Round your answer to two decimal places.
P(A)
the absolute tolerance is +/-0.01

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