Probability

Probability Quiz Review AKS 46/52/47

By Amy Williamson

Study your packet, this review, and the Desmos we worked on! Quiz is tomorrow, May 5th

Follow along on your paper!

This lesson follows your quiz review. Fill in the paper quiz review as you go so that you can check and correct your responses in preparation for your quiz tomorrow!

Multiple Choice

What does the symbol $$\cup$$  stand for?

• Union

• Intersection

• Complement

Multiple Choice

What does the symbol $$\cap$$  stand for?

• Union

• Intersection

• Complement

Multiple Choice

What does the symbol A' or $$A^c$$ stand for?

• Union

• Intersection

• Complement

Multiple Choice

$$A\cup B$$  is...

• All items in both sets

• Only items that overlap

• Items in the Universe that are not in the set

Multiple Choice

$$A\cap B$$  is...

• All items in both sets

• Only items that overlap

• Items in the Universe that are not in the set

Multiple Choice

$$A'$$  is...

• All items in both sets

• Only items that overlap

• Items in the Universe that are not in the set

​​Make sure you know what these symbols stand for!

​Set Notation:

​

Fix your answers as needed!

3A. {3,11}

3B. {3,5,7,9,11,13,15,17}

3C. ​ {1,9,15}

​

Multiple Choice

Use this Venn and the description on your paper to answer the questions.

4a. If 160 students were surveyed, how many students said they did not like watching any of these three sports?

• 19

• 33

• 9

• 15

Multiple Choice

Use this Venn and the description on your paper to answer the questions.

4B. How many students said they enjoy watching lacrosse?

• 13

• 39

• 52

• 15

Multiple Choice

Use this Venn and the description on your paper to answer the questions.

4C. What is the probability a randomly selected student said they like watching soccer and baseball?

• $$\frac{57}{80}$$  

• $$\frac{33}{160}$$  

• $$\frac{3}{20}$$  

• $$\frac{9}{160}$$  

Multiple Choice

Use this Venn and the description on your paper to answer the questions.

4D. What is the probability a randomly selected student said they like to watch only soccer?

• $$\frac{19}{160}$$  

• $$\frac{67}{160}$$  

• $$\frac{33}{160}$$  

• $$\frac{9}{160}$$  

Fix your answers as needed!

4A. 33 because the total is 160 and if you add up all of the numbers on the Venn it isonly 127 so that leaves 33 students who don't like watching any sports.

4B. Add all numbers in Lacrosse: 15+9+15+13 = 52

4C. ​ Soccer AND Baseball overlap is 24+9=33. So 33/160 or .21 or 21%

4D. Only the 19 is in no other circle. So 19/160 or .12 or 12%​

Multiple Select

Select all examples that are mutually exclusive

• Rolling a six or an odd number on a six sided die

• Rolling a six or an even number on a six sided die

• Tossing a coin and getting heads or tails

• Drawing a card and getting a Spade or a Red.

• Drawing a card and getting an Ace or a Heart

Mutually Exclusive events are events that CANNOT happen at the same time. Your three events from the last slide were 1) Six or Odd, 2) Heads or Tails, and 3) Spade or Red Card.

​

Mutually Exclusive

Multiple Choice

7. You roll a fair number cube one time. What is the probability it lands on an even number or a number greater than 2? Is this event Mutually Exclusive?

• Mutually Exclusive

  5/6

• Not Mutually Exclusive

  5/6

• Mutually Exclusive

  7/6

• Not Mutually Exclusive

  7/6

Fix your answers as needed!

6A. Use the General Addition Rule! P(A) + P(B) - P(A and B).

67 + 31 - 20 = 78%

​6B. 67 with a car - ​20 with both = 47% car only

​​6C. 78% own a car or SUV. 100% - 78% = 22%

​

​7. NOT Mutually exclusive, there is overlap. 3/6 + 4/6 - 2/6 = 5/6

Turn the paper over and continue

Multiple Choice

Events A and B are independent. If P(A) = 0.48 and P(B) = 0.15, find P(A and B).

• 0.63

• 0.33

• .072

• 3.2

Multiple Choice

1.     P(A) = 0.45, P(B) = 0.6 and P(A and B) = 0.15.  Are the events A and B independent?  Support your decision mathematically.

• YES!

  $$0.45\times0.6\ne0.15$$  

• NO!

  $$0.45\times0.6\ne0.15$$

• YES!

  $$0.45\times0.6=0.15$$

• NO!

  $$0.45\times0.6=0.15$$

Events whose outcomes do not influence each other.

​

P(A) * P(B) = P(A and B)​

​

​Independent Events: ​

Fix your answers as needed.​

​

1. 0.48x0.15 = 0.072

​

2.​ 0.45x0.6 = 0.27 NOT 0.15 so these are not independent events

​

Multiple Choice

3a. P(right-handed) =

• $$\frac{46}{65}$$  

• $$\frac{13}{65}$$  

• $$\frac{16}{65}$$  

• $$\frac{11}{65}$$  

Multiple Choice

3b. P(junior) =

• $$\frac{46}{65}$$  

• $$\frac{13}{65}$$  

• $$\frac{16}{65}$$  

• $$\frac{11}{65}$$  

Multiple Choice

3c. P(right-handed and junior) =

• $$\frac{46}{65}$$  

• $$\frac{13}{65}$$  

• $$\frac{16}{65}$$  

• $$\frac{11}{65}$$  

Multiple Choice

3d. Based on these probabilities are the events "right-handed batter" and "junior" independent?

• Yes

• No

Fix your answers as needed!

3a. 46/65

3b. 16/65

3c. 11/65

​

3d. (46/65)*(16/65) ≠​ 11/65 so NO these are not independent.

Multiple Choice

4. A fair number cube is rolled three times.

A. What is the probability that the number cube lands on "5" all three times?

• 1/2

• 1/216

• 1/36

• 3/18

Multiple Choice

4. A fair number cube is rolled three times.

A. What is the probability that the number cube lands on "5" at least one time?

• 1/216

• 25/216

• 31/216

• 3/216

Multiple Choice

A bag contains 15 blue cubes, 9 red cubes, and 16 green cubes.  Determine whether the events are independent or dependent, and find each probability.

5. A green cube and then a blue cube are chosen at random with replacement

• Independent

  3/20

• Dependent

  3/20

• Independent

  2/13

• Dependent

  2/13

Multiple Choice

A bag contains 15 blue cubes, 9 red cubes, and 16 green cubes.  Determine whether the events are independent or dependent, and find each probability.

6. Two blue cubes are chosen at random without replacement.

• Independent

  9/64

• Dependent

  7/52

• Independent

  21/160

• Dependent

  15/104

Fix your answers as needed!

​P( one 5 OR two 5's OR 3 5's)