1. COMPOUND EVENTS Grade 7 – Chadwick International School

2. Learning objectives Use the counting principle/tree diagram to know the number of possible outcomes Solve compound event problems

3. Simple Event Compound Events

4. Possible Outcomes Possible Outcomes Event 1 Counting Principle Possible Outcomes Event 2 x

5. Counting Principle Possible Outcomes Event 1 Possible Outcomes Event 2 x x x 46 =24

6. You are buying a new car There are 2 body styles 5 colors available 3 models (luxury model. sports model, standard model) Total Choices = 2 x 5 x 3= 30 possible outcomes

7. Compound Probability Probability Event 1 Probability Event 2 x x x = P(1,red) = 1 6 1 4 1 24 P(1,red) = You roll a die and spin the spinner. What is the P(1,red)?

8. Carlos spins the spinner twice. What is P(orange, brown)? Write your answer as a percentage. Want Total P(orange) = P(orange, brown) P(brown) x x 2 5 P(orange, brown) =

9. Carlos spins the spinner twice. What is P(orange, brown)? Write your answer as a percentage. Want Total P(orange) = P(orange, brown) P(brown) x x 2 5 P(orange, brown) = 2 5 = 4 25 = 16%

10. Ben pick a card. He puts the first card back and picks another card. What is P(green, green)? Write your answer as a percentage. Want Total P(green) = P(green, green) P(green) x x 4 5 P(green, green) =

11. Ben pick a card. He puts the first card back and picks another card. What is P(green, green)? Write your answer as a percentage. Want Total P(green) = P(green, green) P(green) x x 4 5 P(green, green) = 4 5 = 16 25 = 64%

12. 1) A probability experiment consists of rolling a fair number cube numbered 1 through 6 and then spinning a spinner with two equally likely outcomes, red or blue. Find the probability of rolling a 2 on the number cube and spinning red on the spinner. 2) a. A bag contains 6 blue marbles, 4 red marbles, and 2 green marbles. One marble is drawn from the bag, and its color is recorded. Another marble is drawn, and its color is also recorded. What is the probability of drawing 2 blue marbles? B. What is the probability of drawing a blue and red marbles? C. Solve for P(red, green) P(2, red) = 1/12 P(blue, blue) = 1/4 P(blue, red) = 1/6 P(red, green) = 1/18

13. Possible Outcomes Possible Outcomes Event 1 Possible Outcomes Event 2 x Can also be solved using a tree diagram.

14. Possible Outcomes x Outcomes 3 41 2 5 6 12 outcomes H 1H 1T TH 2H 2T T H 3H 3T TH 4H 4T T H 5H 5T TH 6H 6T T

15. 1) Diana picks a marble and flips a coin. How many outcomes are possible? Outcomes H 3 41 2 5 H1 T1 TH H2 T2 T H H3 T3 TH H4 T4 T H H5 T5 T 10 outcomes

16. 2) Jack spins a spinner & picks a marble. How many outcomes are possible? Outcomes B W Y RW B BY BRBW BB Y RW B WY WRWW WB Y RW B RY RRRW RB R 12 outcomes

17. If three coins are tossed, what is the probability of getting exactly two heads? (Draw a tree diagram to get the probability.) P(2 heads) = 3/8 P(2 heads) = 0.375 or 37.5%

18. Jody has four bottles of soft drink – one bottle of cola, one of root beer, one of ginger ale, and one of orange. She chooses three of these bottles to take to a party. If she chooses the ginger ale, what is the probability she also chooses root beer? P(Ginger ale, root beer) = 4/6

19. 1. Find the probability that a family with four children has exactly four girls. Assume that the probability a girl is born is the same as the probability a boy is born. A. What is the probability that the family has two boys and two girls in any order? 2. An automobile dealer has cars available with the combinations of colors (red & blue), engines (4-cylinder & 6-cylinder), and transmissions (manual & automatic. A selection is made at random. A. What is the probability of selecting a car with manual transmission? B. What is the probability of selecting a blue car with manual transmission? C. What is the probability of selecting a car with a 4-cylinder engine and a manual transmission? D. What is the probability of selecting a blue car with a 6-cylinder engine and an automatic transmission?