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**Please only complete this lesson after doing Permutations and Combinations first**

Welcome to the guide on Probability:

Please note this topic is a big differentiator in getting a high score.

*PATH2TJ APPROVED USE ONLY PATH2TJ*

Prerequisites:

The prerequisites are a thorough understanding of Factorials, Permutations, and Combinations. If you do not have a good handle on these concepts, reference our lesson on Permutations and Combinations. It is a crucial lesson to master before starting. If you are having trouble with factorials study the following links first:

● https://www.youtube.com/watch?v=eXcJOgNPYJE

● https://drrossymathandscience.weebly.com/uploads/1/6/6/9/1 6699960/factorials_a_module_1__2_.pdf

All required concepts to do well in the test may not necessarily be emphasized in your classroom, so do not be overwhelmed. In general, the questions will be focused on the probability of independent and dependent events, experimental probability, probability of compound events, and mutually exclusive events. There may also be Venn Diagram based questions and other ways of showing data.

Start by going through these links. Take your time with each one exploring ALL the information they have and trying the questions provided:

1. https://www.youtube.com/watch?v=6IM_M0EltO4 (This instructor starts from the beginning and concisely summarizes the basics)

2. https://www.pbslearningmedia.org/collection/mathcore-sp/#.X lKW0JVYZ9A (there are short videos. We specifically recommend watching Random Coin Toss, Probability Space, and Compound probability)

3. https://www.khanacademy.org/math/cc-seventh-grade-math/c c-7th-probability-statistics (Spend as much time as you can here. Read all the information and attempt all the questions. This is a great resource to learn any math concept.

4. https://www.youtube.com/watch?v=7mQKHB0jL7M&t=1153s (This is a crash course if you feel lost after going through the links above and can’t follow along. Keep in mind this is a lengthy video and gets down to the roots. It also includes some permutations and combinations if you want to learn about those too. **You may skip this video if you did feel confident, though**)

PATH2TJ APPROVED USE ONLY After reviewing the material above, take some time to practice using the link below.

Practice and check your understanding with the practice sheets available here:

● https://www.easyteacherworksheets.com/pages/pdf/math/stats/independentevents/10.html

● https://www.mathworksheetsland.com/topics/logic/venndiagramsset.html

● https://www.easyteacherworksheets.com/pages/pdf/math/stats/compoundprobability/10.html

● https://www.mathworksheetsland.com/stats/16deter/ip.pdf

● https://www.math-drills.com/statistics.php

● https://www.easyteacherworksheets.com/math/stats-co mpoundprobability.html

PATH2TJ APPROVED USE ONLY

Now check if you have mastered this concept by answering the following questions:

1. Anna runs a company where there are 12 employees. 5 of them are male and 7 are female. Two people are chosen at random from the 12 employees. Find the probability that one is a male and one is female.

a. 35/66

b. 1/6

c. 1/36

d. 25/71

2. 20% of the school students are eligible to go to Russia. If a student is eligible, they have a 40% chance of being selected. What is the chance that Ron will not go to Russia even though he is eligible?

a. 40%

b. 60%

c. 8%

d. 5%

3. A square has an area of 81 inches. Inscribed and centered, there is another square of side length 2 inches. If I want to throw a knife, what is the probability it lands outside of the small square (assume there is an equal chance of hitting anywhere on the area of the larger square)?

a. 2/1

b. 4/81

c. 77/81

d. 18/81

4. A survey of 151 people is conducted regarding their favorite Radio station: Radio City, Radio M, and radio life. It was found that every listener of radio M also listens to either Radio City or radio life. The number of people listening to all the radio stations is the same as those who listen to none of the stations. 55 people listen to two stations and 70 people listen to only one station. The number of people who listen to all three stations is…

a. 16

b. 13

c. 9

d. Not enough information is provided

5. Caroline has a dartboard that is 6 inches in radius. She needs a bullseye to win. Assuming she will hit a random part of the board, what is the probability she will get a bullseye if it is 2 inches in diameter?

a. 1/9

b. ⅙

c. 1/25

d. 1/36

6. In a survey of 80 people, 50 of them prefer an arranged marriage. 70 prefer a marriage through love. What are the minimum and the maximum number of people that prefer both types equally, knowing that it is possible for a respondent to prefer neither type of marriage?

a. 40,45

b. 40,50

c. 30,40

d. It cannot be determined from the information provided by

7. Given the following table on color preference, find the probability that a randomly selected person is a male given the color chosen is blue?

a. 53/94

b. 41/221

c. 94/221

d. 29/67 Red Blue Green Female 38 41 36 Male 29 53 24

8. Suppose that the spinner below is spun once. If C represents the outcome, what is the expected value of C?

a. 1

b. 2

c. 3

d. 5

9. My brother will flip a coin 4 times. If I guess the number of heads correctly, he will give me $10. I said that there would be 1 tail. What are my chances of winning $10?

a. ¼

b. ⅙

c. ½

d. 1

10. At a local community center, 72% of its members play golf and Croquet. 80% play Croquet. If a member is selected at random, what is the probability that the member plays croquet given that they are a golfer?

a. 0.90

b. 0.72

c. 0.80

d. 0.58

Answers:

1. A

2. B

3. C

4. D

5. D

6. B

7. A

8. C

9. A

10. A