2. We are learning to: - Enhance Mathematical basic skills knowledge. (Which PLT skills?) -Accurately draw probability trees for independent events and work out probabilities from this. (Grade B) 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

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

4. 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 + 4 When x = -5 Find the mean of: 2, 3, 5, 10 Expand 4(-4x + 5) Write the value of pi to 2d.p. 5) Calculate 6) Find the LCM of 6 and 4. 7) 75% of 24 miles 8) Simplify: 5e + 6y – 7e – 5y 9) Solve: 7(x + 3) = 56 2 9m 6m 3m Calculate the area of the trapezium = =5 (-5) + 4 2 = 29 = = -16x + 20 =3.14 =4 and -4 =12 = = 18 = -2e + y 7x + 21 = 56 7x = 35 x = 5 Area = (a + b)h Area = (6 + 9)3 Area = 22.5cm 2

5. 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 before replacing 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 BEEN REPLACED SO THE PROBABILITY DOES NOT CHANGE ON THE SECOND PICK 3 10 7 3 7 P(B,B) = ALWAYS MULTIPLY THE BRANCHES 10 3 X 3 = 100 9 P(B,G) = 10 3 X 7 = 100 21 P(G,B) = 10 7 X 3 = 100 21 P(G,G) = 10 7 X 7 = 100 49 P(The same colour) = P(B,B) + P(G,G) = 100 9 + 49 = 100 58 = 50 29 P(BG in any order) = P(B,G) + P(G,B) = 100 21 + 100 21 = 100 42 = 50 21

6. PROBABILITY TREES Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK (GRADE B) Fill in the probability tree below to display the outcomes of flipping a fair coin twice: 2 nd 1 st H …… …... T ….... P(H,H)=………………… P(H,T)=……………….... P(T,H)=……………….... P(T,T)=…………………. Flip 1) 1 2 T H T H 2 1 2 1 2 1 2 1 2 1 2 1 X 2 1 = 4 1 2 1 X 2 1 = 4 1 2 1 X 2 1 = 4 1 2 1 X 2 1 = 4 1

7. PROBABILITY TREES Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK (GRADE B) 2) Q1 beads black green First Choice Second Choice black green black green Rebecca has nine coloured beads in a bag. Four of the beads are black and the rest are green. She removes a bead at random from the bag and notes the colour before replacing it. She then chooses a second bead. (a) Draw a tree diagram showing all possible outcomes. (b) Calculate the probability that Rebecca chooses: (i) 2 green beads (ii) A black followed by a green bead (iii) The same colour. P(same colour) = 81 16 + 81 25 = 81 41

8. P(E,E) = PROBABILITY TREES Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK (GRADE B) 3) Q1 beads (a) Complete a tree diagram to show all the probabilities of obtaining even and odd numbers. (b) Calculate the probability of spinning two numbers which multiply to given an even number. Even Odd 2 5 3 5 Even Odd Even Odd 2 5 3 5 2 5 3 5 5 2 X 5 2 = 25 4 P(E,O) = 5 2 X 5 3 = 25 6 P(O,E) = 5 3 X 5 2 = 25 6 P(O,O) = 5 3 X 5 3 = 25 9 P(EE) + P(EO) + P(OE) P(Spinning two numbers which multiply to make an even) = = ++ =

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) 1) Q1 beads Peter and Becky run a race and play a tennis match. The probability that Peter wins the race is 0.4. The probability that Becky wins the tennis is 0.7. (a) Complete the tree diagram below. (b) Use your tree diagram to calculate (i) the probability that Peter wins both events. (ii) The probability that Becky loses the race but wins at tennis. Becky Win Peter Win Becky Win Race Tennis Peter Win 0.4 0.7 0.6 0.3 0.7 0.4 x 0.3 = 0.12 0.4 x 0.7 = 0.28 0.6 x 0.3 = 0.18 0.6 x 0.7 = 0.42 P(Win and Win) for Peter = 0.12 P(Lose and Win) for Becky = 0.28

10. 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 Peter has ten coloured cubes in a bag. Three of the cubes are red and seven are blue. He removes a cube at random from the bag and notes the colour but does not replace it. He then chooses a second cube at random. Record the information in a tree diagram. red blue First Choice Second Choice red blue red blue

11. 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 independent events and work out probabilities from this. What grade are we working at?

12. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? PLENARY ACTIVITY – GRADE B EXAMINATION QUESTION Weather records are kept in a town called Snowville. They show that in a typical April it snows on 20 days out of the 30 days in the month. PROBABILITY TREES (a) Complete a fully labelled tree diagram showing the probabilities of it snowing or not snowing on the first two Sundays in April in Snowville. (b) Calculate the probability that it snows on only one of these two Sundays. You must show your working. (4 marks) (3 marks) FIRST SUNDAY SECOND SUNDAY SNOW NOT SNOW SNOW NOT SNOW SNOW NOT SNOW = = P(S,S) = 3 2 X 3 2 = 9 4 P(S,NS) = 3 2 X 3 1 = 9 2 P(NS,S) = 3 1 X 3 2 = 9 2 P(NS,NS) = 3 1 X 3 1 = 9 1 P(S,NS or NS, S) = 9 2 + 9 2 = 9 4

13. Draw your brain What have you learnt? In your brain, write or draw everything you can remember about drawing probability trees for independent 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