Day 6 Quiz Review and Quiz Day! CCM2 Unit 6: Probability

For #1 and 2, show ALL work by hand with the formulas! Warm-up For #1 and 2, show ALL work by hand with the formulas! 1. The ski club with ten members is to choose three officers captain, co-captain, and secretary. How many ways can those offices be filled? 2. You are on your way to Hawaii and of 15 possible books, you can only take 10. How many different collections of 10 books can you take? 3. Dominoes offers a deal that says you can order a pizza with at most 5 toppings for $9.99. If there are a total of 12 types of toppings, how many different pizzas could you order? 4. On a fair dice, what is the probability of rolling a multiple of 3 or a number greater than 4? Are these events mutually inclusive or exclusive? A family who breeds dogs made the following observations: - 30% of their dogs are males - 15% of females are brown colored - 56% of males are not brown colored What is the probability there is a brown male?

Warm-up Answers 1. The ski club with ten members is to choose three officers captain, co-captain, and secretary. How many ways can those offices be filled?    2. You are on your way to Hawaii and of 15 possible books, you can only take 10. How many different collections of 10 books can you take?   3. Dominoes offers a deal that says you can order a pizza with at most 5 toppings for $9.99. If there are a total of 12 types of toppings, how many different pizzas could you order? 4. On a fair dice, what is the probability of rolling a multiple of 3 or a number greater than 4? Are these events mutually inclusive or exclusive? A family who breeds dogs made the following observations: -30% of their dogs are males - 15% of females are brown colored -56% of males are not brown colored What is the probability there is a brown male? 10P3 = 210 15C10 = 3003 12C5+12C4+12C3+12C2+12C1+12C0 = 1586 2/6 + 2/6 – 1/6 = 3/6 = 1/2 Mutually Inclusive 0.132 = 13.2% (use tree diagram)

Homework Answers 1. (2/52)(26/51)/(2/52) = 26/51 = .5098 51% 1. (2/52)(26/51)/(2/52) = 26/51 = .5098 51% 2. (2/52)(26/51)/(2/52) = 26/51 = .5098 51% 3. 0.25/0.55 = 5/11 = .456 = 45.6% 4. 0.15/0.45 = 1/3 = .333 = 33.3% 5. (8/16)x(7/15) = 7/30 = 23.3% 6. (8/16) x (3/15) = 1/10 = 10% 7. a) 714/1375 b) 661/1375 c) 128/293 d) 438/661

Homework Answers 8. a) 78/663 = 2/17 = 11.8% b) 561/ 663 = 11/13 = 85% c) 78/165 = 26/55 = 47% d) 175/498 = 35% 9. a) 15/28 = 54% b) 1/2 = 50% c) 7/15 = 47% d) 6/14 = = 3/7 = 43%

Homework Answers 1. a.) on next slide b.) 9/36 = 1/4 c.) 27/36 = 3/4 d.) no because they do not have an equal probability 2. a.) on next slide b.) 6/16 = 3/8 c.) 10/16 = 5/8 d.) no because the probabilities are not equal 3.) 10*9*8 = 720 4.) ½ 5.) 8/36 = 2/9 6.) 11/35 7.) 7,980,000 8.) The probability of pulling out a total of $2 is greater. 9.) a.) 5/22 b.) 5/22 10.) 21/22

2a.) 1A) Pt to B A

11a.) 0.30 0.12 0.28 60% Coach Sam 50% Goal Keeper Not Goal Keeper 40 % Coach Alex 30% Goal Keeper Not Goal Keeper 70%

Homework Answers 11. b.) (.6 x .5) + (.4 x .3) = .42 (42%) c.) 50% d.) P(C Alex & not GK) = (0.4)(0.7) = 0.483 P(not GK) (0.6)(0.5) + (0.4)(0.7) 12. 12.8% 13. 1/26 14. a.) 58/79 b.) 21/79 c.) 14/35 = 2/5

HW Answers 1. 17/70 = 24.3% 2. 3/10 = 30% 3. 1/3 = 33.3% 4. 3/7 = 42.9% 5. 13/31 = 41.9% 6. 9/25 = 36% 7. 1700 8. 1/5 = 20% Experimental because data was collected Yes. The ad is saying gum helps your teeth by saying dentists recommend chewing it. Answers will vary. Ex/ They could survey more dentists. 10 dentists is not a representative sample.

Quiz Review When rolling a die twice, find the probability of rolling an even number then a multiple of 3. When rolling a die once, find the probability of rolling an even number or a multiple of 3. Jack is a student in Bluenose High School. He noticed that a lot of the students in his math class were also in his chemistry class. In fact, of the 60 students in his grade, 28 students were in his math class, 32 students were in his chemistry class, and 15 students were in both his math class and his chemistry class. a) Draw a Venn diagram and help Jack with his calculations. b) Calculate P(math U chemistry) c) Calculate P(math  chemistry) d) Calculate the probability of selecting a student at random who was either in his math class or his chemistry class, but not both. e) Calculate P(Jack’s Class c) Finish here if not finished on Day 5

Quiz Review Answers When rolling a die twice, find the probability of rolling an even number then a multiple of 3. 2) When rolling a die once, find the probability of rolling an even number or a multiple of 3. P(even) * P(mult. of 3) = 3/6 * 2/6 = 6/36 = 1/6 Mutually Inclusive Events P(even) + P(mult. of 3) – P(even & mult. of 3) = 3/6 + 2/6 - 1/6 = 4/6 = 2/3

Quiz Review Answers Jack is a student in Bluenose High School. He noticed that a lot of the students in his math class were also in his chemistry class. In fact, of the 60 students in his grade, 28 students were in his math class, 32 students were in his chemistry class, and 15 students were in both his math class and his chemistry class. a) Draw a Venn diagram and help Jack with his calculations. b) Calculate P(math U chemistry) c) Calculate P(math  chemistry) d) Calculate the probability of selecting a student at random who was either in his math class or his chemistry class, but not both. e) Calculate P(Jack’s Class c) Class 15 Math 13 Chemistry 17 15 45/60 = ¾ 15/60 = ¼ 30/60 = ½ 15/60 = ¼

Quiz Review Activity! Activity could be done with Whiteboards OR You could post 2 on a page as an around the room game (to do that, move up the last answer slide before the first question, print 2 pages on 1 so the answers are on top, then scramble questions)

Given the following Venn Diagram, how many students are taking an art AND a music class?

6

Given the following Venn Diagram, how many students are taking an art OR a music class?

38

Given the following Venn Diagram, how many students are in the Venn Diagram?

140

P(art AND music) = ________ Given the following Venn Diagram, find the PROBABILITY that a student is taking an art AND a music class. P(art AND music) = ________

6/140 or 3/70

P(art OR music) = ________ Given the following Venn Diagram, find the PROBABILITY that a student is taking an art OR a music class. P(art OR music) = ________

38/140 or 19/70

P(A) + P(AC) = ___________ The probability of an event + the probability of its complement = ________ P(A) + P(AC) = ___________

1

The probability of rain tomorrow is 40% The probability of rain tomorrow is 40%. What is the probability that it doesn’t rain?

0.60

The probability of rain tomorrow is 40%. What are the odds of rain?

4:6 or 2:3

What is the probability that a student is a female AND a sophomore? At SWGHS, 30% of the students are sophomores. 48% of the students are female. What is the probability that a student is a female AND a sophomore?

14.4%

A coin and a die are tossed/rolled A coin and a die are tossed/rolled. What is the probability of getting tails and a 4.

1/12

If the probability of receiving a piece of mail is 25% on any given day, what is the probability of receiving a piece of mail today and no mail tomorrow?

18.75%

Given a standard deck of cards, what is the probability of drawing a diamond?

25%

Given a standard deck of cards, what is the probability of drawing a king?

1/13

Given a standard deck of cards, what is the probability of drawing the king of diamonds?

1/52

Given a standard deck of cards, what is the probability of drawing a king OR a diamond?

16/52 or 4/13

Given a standard deck of cards, what are the ODDS of drawing a diamond?

13:39 or 1:3

Quiz Time!!