# Introduction to Probability (Math Problem Sample)

Problems need to include all required steps and answer(s) for full credit. All answers need to be reduced to lowest terms where possible.

Answer the following problems showing your work and explaining (or analyzing) your results.

In a poll, respondents were asked if they have traveled to Europe. 68 respondents indicated that they have traveled to Europe and 124 respondents said that they have not traveled to Europe. If one of these respondents is randomly selected, what is the probability of getting someone who has traveled to Europe?

The data set represents the income levels of the members of a golf club. Find the probability that a randomly selected member earns at least $100,000.

INCOME (in thousands of dollars)

98 102 83 140 201 96 74 109 163 210

81 104 134 158 128 107 87 79 91 121

A poll was taken to determine the birthplace of a class of college students. Below is a chart of the results.

What is the probability that a female student was born in Orlando?

What is the probability that a male student was born in Miami?

What is the probability that a student was born in Jacksonville?

Gender Number of students Location of birth

Male 10 Jacksonville

Female 16 Jacksonville

Male 5 Orlando

Female 12 Orlando

Male 7 Miami

Female 9 Miami

Of the 538 people who had an annual check-up at a doctor’s office, 215 had high blood pressure. Estimate the probability that the next person who has a check-up will have high blood pressure.

Find the probability of correctly answering the first 4 questions on a multiple choice test using random guessing. Each question has 3 possible answers.

Explain the difference between independent and dependent events.

Provide an example of experimental probability and explain why it is considered experimental.

The measure of how likely an event will occur is probability. Match the following probability with one of the statements. There is only one answer per statement.

0 0.25 0.60 1

a. This event is certain and will happen every time.

b. This event will happen more often than not.

c. This event will never happen.

d. This event is likely and will occur occasionally.

Flip a coin 25 times and keep track of the results. What is the experimental probability of landing on tails? What is the theoretical probability of landing on heads or tails?

A color candy was chosen randomly out of a bag. Below are the results:

Color Probability

Blue 0.30

Red 0.10

Green 0.15

Yellow 0.20

Orange "?

a. What is the probability of choosing a yellow candy?

b. What is the probability that the candy is blue, red, or green?

c. What is the probability of choosing an orange candy?

Module 1 - Case: Introduction to Probability

Name

Institution

Date

Answer the following problems showing your work and explaining (or analyzing) your results.

In a poll, respondents were asked if they have traveled to Europe. 68 respondents indicated that they have traveled to Europe and 124 respondents said that they have not traveled to Europe. If one of these respondents is randomly selected, what is the probability of getting someone who has traveled to Europe?

Probability= Number of favorable outcomes/ Total number of outcomes

Total number of respondents =68+124=192

Probability=68/192= 0.35

The data set represents the income levels of the members of a golf club. Find the probability that a randomly selected member earns at least $100,000.

INCOME (in thousands of dollars)

98 102 83 140 201 96 74 109 163 210

81 104 134 158 128 107 87 79 91 121

IncomeIncome000'Probability000'Probability740.051070.05790.051090.05810.051210.05830.051280.05870.051340.05910.051400.05960.051580.05980.051630.051020.052010.051040.052100.05

There are 20 observations and for each income level the probability is 0.05(1/20)

Probability that one earns at least $100,000= 0.06

A poll was taken to determine the birthplace of a class of college students. Below is a chart of the results.

What is the probability that a female student was born in Orlando?

Probability= Number of favorable outcomes/ Total number of outcomes

=12/59= 0.2

What is the probability that a male student was born in Miami?

Probability= Number of favorable outcomes/ Total number of outcomes

=7/59= 0.12

What is the probability that a student was born in Jacksonville?

Probability= Number of favorable outcomes/ Total number of outcomes

=26/59=0.44

GenderNumber of studentsLocation of birthMale10JacksonvilleFemale16JacksonvilleMale5OrlandoFemale12OrlandoMale7MiamiFemale9MiamiOf the 538 people who had an annual check-up at a doctor’s office, 215 had high blood pressure. Estimate the probability that ...

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