1. We are learning to: - Enhance Mathematical basic skills knowledge. (Which PLT skills?) -Accurately draw probability trees for dependent events and work out probabilities from this. (Grade A*) Always aim high! LESSON OBJECTIVES Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? AUTHOR Where are we in our journey? Real life cross/curricular links? www.mistrymaths.co.uk

2. LEARNING JOURNEY Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills

3. STARTER Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXTENSION TASK 1) 2) 3) 4) x - 7 When x = -6 Find the median of: 2, 4, 7, 11 Expand 5(-3x + 2) Write the value 5 cubed. 5) Calculate 6) Find the HCF of 18 and 30. 7) 25% of 36 miles 8) Simplify: 5e + 8y – 9e – 7y 9) Solve: 8(x + 4) = 56 2 11m 7m 4m Calculate the area of the trapezium = 5.5 (-6) - 7 2 = 29 = = -15x + 10 =125 =7 and -7 =6 = = 9 = -4e + y 8x + 32 = 56 8x = 24 x = 3 Area = (a + b)h Area = (7 + 11)4 Area = 36m 2

4. Hubert has 10 coloured counters in a bag. Three of the counters are blue and seven of the counters are green. He removes a counter at random from the bag and notes the colour and does not replace it. He then chooses a second counter. Record the information on a tree diagram and work out the probabilities of the different outcomes. PROBABILITY TREES Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXAMPLE Blue Green 3 10 FIRST PICK 7 10 SECOND PICK Blue Green Blue Green COUNTERS HAVE NOT BEEN REPLACED SO THE PROBABILITY DOES CHANGE ON THE SECOND PICK 2 9 7 9 3 9 6 9 P(B,B) = ALWAYS MULTIPLY THE BRANCHES 10 3 X 9 2 = 90 6 P(B,G) = 10 3 X 9 7 = 90 21 P(G,B) = 10 7 X 9 3 = 90 21 P(G,G) = 10 7 X 9 6 = 90 42 P(The same colour) = P(B,B) + P(G,G) = 90 6 + 42 = 90 48 = 15 8 P(BG in any order) = P(B,G) + P(G,B) = 90 21 + 90 21 = 90 42 = 15 7

5. PROBABILITY TREES Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK (GRADE A*) 1) Q1 beads Lucy has a box of 30 chocolates. 18 are milk chocolate and the rest are dark chocolate. She takes a chocolate at random from the box and eats it. She then chooses a second. Draw a tree diagram to show all the possible outcomes. Milk First Pick Second Pick Dark P(Milk and Milk) = P(Milk and Dark) = P(Dark and Milk) = P(Dark and Dark) = Dark Milk Dark Milk

6. PROBABILITY TREES Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK (GRADE A*) 2) Q1 beads Jimmy has five coloured counters in a bag. Two of the counters are blue and the rest are red. He removes a counter at random from the bag and notes the colour but does not replace it. He then chooses a second counter. Draw a tree diagram showing all possible outcomes. (a) P(Blue,Blue) = (b) P(Red,Red) = (c) P(One blue and one red in any order) = Blue Red 2 5 FIRST PICK 3 5 SECOND PICK Blue Red Blue Red COUNTERS HAVE NOT BEEN REPLACED SO THE PROBABILITY DOES CHANGE ON THE SECOND PICK 1 4 3 4 2 4 2 4 P(B,B) = ALWAYS MULTIPLY THE BRANCHES 5 2 X 4 1 = 20 2 P(B,R) = 5 2 X 4 3 = 20 6 P(R,B) = 5 3 X 4 2 = 20 6 P(R,R) = 5 3 X 4 2 = 20 6 2 = 10 1 20 6 = 10 3 20 6 + 6 = 12 = 5 3

7. PROBABILITY TREES Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK (GRADE A*) 3) Q1 beads The probability Manchester City will win the Premiership is 0.7. If they do, the probability they will go on to win the F.A. Cup is 0.6. But if they dont, its only 0.5. Draw a tree diagram to represent this information. Use a tree diagram to find the probability that they win (a) the double (b) only one of them Win Lose 0.7 PREMIERSHIP FA CUP Win Lose Win Lose P(W,W) = ALWAYS MULTIPLY THE BRANCHES P(W,L) = P(L,W) = P(L,L) = 0.3 0.6 0.4 0.5 0.7 x0.6= 0.42 0.7 x0.4= 0.28 0.3 x0.5= 0.15 0.3 x0.5= 0.15 P(Double) = 0.42 P(Only one W) = 0.28 + 0.15 = 0.43

8. PROBABILITY TREES Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXTENSION (GRADE A*) 1) Q1 beads A shop offers a package where customers can choose either a video player or a DVD player or a Hi-fi system and either a flat screen or a normal screen television. Over a period of time, 35% of the customers choose a video player and 60% choose a DVD player. The rest choose a Hi-fi system. Independently 75% of the customers choose flat screen televisions. (a) Complete the tree diagram below: (b) All customers were entered into a prize draw. What is the probability that the winner bought a Hi-Fi system with a normal screen television? 0.05 Probability adds up to one whole 0.25 P(H,N) = 0.05 x 0.25 = 0.0125

9. PROBABILITY TREES Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXTENSION (GRADE A*) 2) Q1 beads Sports activities are held after school. Zoe attends these classes on Monday and Wednesday. She can choose one of badminton, dance or netball on each day. The probability she chooses badminton is 0.5. The probability she chooses dance is 0.4. Assume Zoes choices are independent. (a) Complete the tree diagram below: (b) What is the probability Zoe will choose the same sports activity on both days? 0.1 Probability adds up to one whole 0.1 P(B,B) = 0.5 x 0.5 = 0.25 P(D,D) = 0.4 x 0.4 = 0.16 P(N,N) = 0.1 x 0.1 = 0.01 P(Same sport) = 0.25+ 0.16 + 0.01 = 0.42

10. DISCOVERY Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills LINK BACK TO OBJECTIVES - Accurately draw probability trees for dependent events and work out probabilities from this. What grade are we working at?

11. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? PLENARY ACTIVITY – ROCK, PAPER AND SCISSORS PROBABILITY TREES Complete a fully labelled tree diagram to shows the outcomes of a rock, paper and scissors game between two players. TASK

12. P(Draw) = Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? PLENARY ACTIVITY PROBABILITY TREES Player A Scissors Paper Stone Scissors Paper Stone Scissors Paper Stone Scissors Paper Stone Player B Draw A Wins B Wins Draw A Wins B Wins Draw 1/9 1/3 x 1/3 = 1/9 P(A Wins) = 1/9 + 1/9 + 1/9 = 3/9 = 1/3 P(B Wins) = 1/9 + 1/9 + 1/9 = 3/9 = 1/3 1/3

13. Draw your brain What have you learnt? In your brain, write or draw everything you can remember about drawing probability trees for dependent events. It can be a skill or a reflection, or something else that might be prominent in your brain. What grade are we working at? Where are we in our journey?

14. . How well do you understand the task? I dont understand I nearly understand I fully understand Creative Entrepreneur Responsible Citizen Independent Learner Positive Thinker Team Worker Reflective Learner Enterprise Skills Which ones are you using? SELF ASSESSMENT Plenary Activity www.mistrymaths.co.uk

15. SELF ASSESSMENT Plenary Activity On your post it notes… Think about how you can improve your work. On your post it notes… Think about how you can improve your work. WWW (What Went Well) EBI (Even Better If) Creative Entrepreneur Responsible Citizen Independent Learner Positive Thinker Team Worker Reflective Learner Enterprise Skills Which ones are you using? www.mistrymaths.co.uk