# Probability, Chance & Fundamental Counting Techniques Chapter Exam

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!

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Question 1
1.
Let F = {2, 5, 7, 9}

Let G = {1, 4, 6, 8}

Which of the following is true?

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Question 2
2.
Let set A = {socks, shoes, pants, shorts}.

Let set B = {shorts, sandals, t shirt}

Find.

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Question 3
3.
Given A = {1, 2, 3, T, U, B, E}

Which of the following is an element of set A?

#### Question 4 4. Tim and Joey have a toy train consisting of a single locomotive car and eight different carriages. In how many different ways can Tim and Joey form a train, keeping in mind that the locomotive car must be the first car in the train?

#### Question 5 5. How many different, six-letter arrangements can we form using the letters of the word 'person,' given that each arrangement must contain all six letters?

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#### Question 6 6. A hacker wants to find a customer's 5-digit PIN-code. How many different arrangements are there, given that the person who has the account may have used any given digit more than once when setting up the PIN-code?

#### Question 7 7. A history teacher gave his class a five-question multiple choice test. Each question has four possible answers: A, B, C, or D. Assume that each question has to be answered and each answer must be one of the four choices. How many distinct test papers are in the sample space?

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Question 8
8.
You are given the following set of outcomes for a coin-tossing experiment (note: T is tail and H is head).

E = { TT, TH, HT }

Describe the experiment that produced the event (E).

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Question 9
9.
A teenage girl is trying to put together her fall outfits. Each outfit consists of one top, one bottom and one accessory. The list below shows the pieces of clothing that she has in her closet.

TOPS - sweater, hoodie, long-sleeved blouse, polo shirt

BOTTOMS - pants, skirt

ACCESSORIES - scarf, headband, beret

How many different outfits are in the sample space AND what proportion of all the different outfits have the hoodie as the top?

#### Question 10 10. There are two ways to play a game and win. Each comes with its own probability of winning. Game option A has a probability of 1/4 and game option B has a probability of 1/8. Which option has the higher probability?

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#### Question 11 11. What is the probability of rolling either a 3 or a 6 when rolling a die?

#### Question 12 12. A probability of 1 means what?

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Question 13
13.
Kyle works at a local music store. The store receives a shipment of new CDs in a box. In the shipment, there are 10 country CDs, 5 rock CDs, 12 hip hop CDs, and 3 jazz CDs.

What is the probability that the first CD that Kyle pulls from the box will NOT be hip hop?

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Question 14
14.
Kyle works at a local music store. The store receives a shipment of new CDs in a box. In the shipment, there are 10 country CDs, 5 rock CDs, 12 hip hop CDs, and 3 jazz CDs.

What is the probability that Kyle will select a jazz CD from the box, and then, without replacing the CD, select a country CD?

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Question 15
15.
Kyle works at a local music store. The store receives a shipment of new CDs in a box. In the shipment, there are 10 country CDs, 5 rock CDs, 12 hip hop CDs, and 3 jazz CDs.

What is the probability that the first CD Kyle chooses from the box will be country?

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#### Question 16 16. Suppose you can choose from 3 different shirts, 2 pairs of pants, and 5 pairs of shoes. Use the fundamental counting principle to find out how many different outfit combinations you can make.

#### Question 17 17. Find the situation in which you could NOT use the fundamental counting principle.

#### Question 18 18. If you have a combination lock that consists of three numbers, and each number in the combination has 10 options (the digits 0 to 9), how many combinations can you create?

#### Question 19 19. The area model shows the possible outcomes from flipping a coin and rolling a six-sided die. What is the probability of flipping heads AND rolling an even number?

#### Question 20 20. Using compound probability, determine the probability of spinning an odd number on one spinner and the color brown on the other.

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#### Question 21 21. With these tiles faced down, what is the probability of pulling a letter 'T' from these tiles?

#### Question 22 22. How many ways are there to choose five apples from 14 apples?

#### Question 23 23. Find 8!

#### Question 24 24. Your local candy store offers 12 different colors of hard candies. The deal of the day allows you to choose four cups of candies, with each cup representing one color of candy. As you can have more than one cup of the same color, how many ways are there to do this?

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Question 25
25.
Let set M = {1, 3, 4, 5}

Let set R = {4, 6, 7}

Find.

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#### Question 26 26. At a charitable event, three raffle tickets are drawn from a total of 100, for first, second and third prizes. How many different ways are there for drawing the three winning tickets?

#### Question 27 27. A coin is tossed three times. For each toss, the possible outcomes are H (Heads) or T (Tails). What is the sample space for this experiment?

#### Question 28 28. What is the probability of picking a blue balloon if there are 3 blue balloons, 1 red balloon, and 1 yellow balloon?

#### Question 29 29. The probability of winning a prize at a ball toss at a carnival is 2/7. What is the probability of not winning a prize?

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Question 30
30.
How many ways can you create a workout (exercise) plan if you have to choose one each from:

10 flexibility exercise

5 lower body exercises

7 upper body exercises

#### Probability, Chance & Fundamental Counting Techniques Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!