Name: ______Date: ______Academic: ___

Probability Review

I can find probabilities of compound events using organized lists, two-way tables, tree diagrams, and simulations.

Indicate how you feel with:

  • Organized Lists:
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  • Tree Diagrams:

  • Two-Way Tables:
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  • Simulations:

1)Stephen has a spinner and a number cube similar to the ones below. After spinning and rolling the number cube, he will add the two numbers.

What is the probability that the sum of the numbers from the spinner and number cube will be 6 or 8?

2)What would be the total number of outcomes for each sample space? You may use a tree diagram or the counting principle.

a)choosing a hamburger or hot dog and potato salad or macaroni salad

b)choosing a vowel from the word COMPUTER and a consonant from the word BOOK

  1. What is the probability of selecting two O’s?

c)choosing between the numbers 1, 2 or 3, and the colors blue, red, or green

  1. What is the probability of getting a prime number and a primary color?

d)Dana has nine pairs of shoes. She wants to organize them in her closet so that they are placed in a row. In how many different ways can Dana arrange nine pairs of shoes in a row? The pairs will not be separated.

State
California
Idaho
Montana
Oregon
Washington

e)Katy’s family is planning a trip around the United States. If they want to visit each state listed in the table, how many different orders can they do so?

f)a license plate that has 3 numbers from 0 to 9 and 2 letters where each number and a letter may not be used more than once

g)tossing 4 coins

3)Jerry played a game where he spun each of the spinners shown once. If he spins an odd number on Spinner 1, red or blue on Spinner 2, and an A on Spinner 3, how many possible unique outcomes are there?

4)I flip three coins.

a)Draw a tree diagram representing the sample space.

b)Determine the probability of getting exactly two tails.

c)Determine the probability of getting at least two tails.

5)At a state fair, there are 10 animal exhibits, 12 gardening exhibits, and 8 farm equipment exhibits. Describe a model that you could use to simulate randomly choosing an exhibit to visit.

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6)Describe a situation that you could use to answer a 15-question quiz, if five questions are true or false questions and the remaining questions are multiple choice with four options.

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7)During the grand opening of a fast food restaurant, every person that comes to the restaurant receives a prize. There are 6 different prizes. Describe a model that could be used to simulate which prizes the first 75 customers will receive.

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8)Ricardo surveyed 110 eighth grade students to find out if they have a part time job. There are 60 students who have a part-time job, including 48 honor roll students. Half of the students who do not have a job are on the Honor Roll. Construct a two-way table summarizing the data. Find and interpret the relative frequencies by column. Round to the nearest hundredth if necessary.

9)Customers entering a store were asked what electronic technology they own. The results of the survey are shown at the right.

a)Find and interpret the relative frequencies by row. Round to the nearest hundredth if necessary.

10)The two-way table shows how some students get their news.

a)How many students were surveyed? ______

b)What is the relative frequency, written as a percent, of 7th grade students who watch TV to the total number of students who watch TV? ______

11)The table which shows the number of male and female who like different types of cars.

a)Find the relative frequency of male and female who like sports cars. Write as a decimal. ______

b)Find and interpret the relative frequencies by row. Write your answers as decimals rounded to the nearest hundredth.

12)A family has two children. Draw a tree diagram to show the sample space of the children’s genders. Then determine the probability of the family having two girls.

13)You are trying to decide which pizza to order for dinner. Your choices for crust are: regular, thin, and deep dish. You want only one topping and will choose either pepperoni or sausage. Determine the number of outcomes.

  1. How would your sample space change if you added bacon as a third topping choice?

14)a. The telephone extensions at MCMS use 4 digits. How many extensions are possible if there are no restrictions?

  1. How many extensions are possible if the first digit cannot be 0 or 9?

15)What is the sample space (number of outcomes) if I flip a coin twice and spin a spinner with four sections three times?

16)a. Each person that works at a company is given a 5-digit code followed by 3 letters. These employees must enter their codes on a keypad to enter and exit the office building. How many codes are possible if there are no restrictions?

  1. How many passwords are possible if no letter or digit can be repeated?

17)a. You are choosing a computer password. The password has 3 lowercase letters followed by 2 digits. How many passwords are possible if there are no restrictions?

b. How many passwords are possible if no letter or digit can be repeated?

18)What is the sample space (number of outcomes) if I pick a number from 1 to 20 and a letter from the alphabet?

TravelTime

A travel agent plans trips for tourists fromChicago to Miami.He gives themthree ways toget from town to town:airplane, bus, train.Once the tourists arrive, there are twowaysto get to the hotel: hotel van or taxi.The cost of each type of transportation is given in the table below.

TransportationType / Cost
Airplane / $350
Bus / $150
Train / $225
Hotel Van / $60
Taxi / $40

1.Draw a tree diagramto illustrate the possible choices for the tourists.Determine the cost for each outcome.

2.If these six outcomes are chosen equally by tourists, what is the probability that a randomly selected tourist travel in a bus?

3.What is the probability that a person’s trip cost less than $300?

4.What is the probability that a person’s trip costs more than $350?

5.If the tourists were flying to New York, the subway would be a third way to get to the hotel.How would this change the number of outcomes?Use the Fundamental Counting Principle to explain your answer.