1. We are learning to: - Enhance Mathematical basic skills knowledge. (Which PLT skills?) -Accurately calculate the probability of independent events. (Grades B-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 - 2x When x = -3 Find the median of: 3, 6, 9, 12 Expand -5(-4x - 3) 5) Calculate 11 6) Find the LCM of 8 and 4. 7) 50% of 40miles 8) Simplify: 8e + 6y – 9e + 7y 9) Solve: 6(x + 8) = 60 2 11m 9m 2m Calculate the area of the trapezium = 7.5 (-3) -2 X -3 2 = 15 = = 20x + 15 =5 = 11 x 11 =8 = 20miles = -e + 13y 6x + 48 = 60 6x = 12 x = 2 Area = (a + b)h Area = (9 + 11)2 Area = 20m 2 2 =121

4. The chance that Ashley hits a target with an arrow is. He has two shots at the target. What is the probability of each of these outcomes? INDEPENDENT EVENTS Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXAMPLE Independent Events AND X OR + (a) Hits target both times (b) Hits target only once(c) Hits target at least once P(Hits both times) P(1 st hits 2 nd hits) This is the same as and x P(Hits both times) = 16 1 P(Hits target once only) P( 1 st hits,2 nd misses 1 st misses,2 nd hits ) This is the same as or + xx P(Hits target once only) = 16 3 + 3 6 8 3 P(Hits target once only) = P(Hits at least once) This is the same as Worked out in (a) Worked out in (b) + + =

5. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK (GRADE B) 1) Alf tosses a coin twice. The coin is biased so it has a probability of two-thirds of landing on a head. What is the probability that he gets: (a) two heads (b) a head and a tail (in any order)? Bernice draws a card from a pack of cards, replaces it, shuffles the pack and then draws another card. What is the probability that the cards are: (a) both Aces (b) an Ace and a King (in any order)? The probability that I am late for work on Monday is 0.4. The probability that I am late on Tuesday is 0.2. What is the probability of each of the following outcomes? (a) I am late for work on Monday and Tuesday. (b) I am late for work on Monday and on time on Tuesday. (c) I am on time on both Monday and Tuesday. A dice is thrown twice. What is the probability that both scores are: (a) even (b) one even and one odd (in any order)? A bag contains 15 white beads and 10 black beads. I take out a bead at random, replace it and take out another bead. What is the probability that: (a) both beads are black (b) one bead is black and the other white (in any order)? I throw a dice three times. What is the probability of getting three sixes? 2) 3) 4) 5) 6) INDEPENDENT EVENTS = = 0.48

6. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXTENSION (GRADE A) 1) 2) 3) 4) INDEPENDENT EVENTS Explain why picking a red card from a pack of cards and picking a King from a pack of cards are not independent events. Ronda has to take a three-part language examination paper. The first part is speaking. She has a 0.7 chance of passing this part. The second part is listening. She has a 0.6 chance of passing this part. The third part is writing. She has a 0.8 chance of passing this part. (a) If she passes all three parts, her father will give her £20. What is the probability that she gets the money? (b) If she passes two parts only, she can resit the other part. What is the chance she will have to resit? (c) If she fails all three parts, she will be thrown off the course. What is the chance she is thrown off the course? Roy regularly goes to Bristol by train. The probability of the train arriving in Bristol late is 0.05. The probability of it raining in Bristol is 0.8. What is the probability of: (a) Roy getting to Bristol on time and it not raining (b) Roy travelling to Bristol five days in a row and not being late at all (c) Roy travelling to Bristol three days is a row and it raining every day? What is the probability of rolling the same number on a dice five times in a row? = 0.336 = 0.452 = 0.024 = 0.19 = 0.77 = 0.512 Red cards can also be kings so it becomes dependent

7. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? MINI-PLENARY ACTIVITY INDEPENDENT EVENTS http://www.youtube.com/watch?v=5GGnHHjG1Uc Watch the roulette video. What is the probability of them winning? AMERICAN ROULETTE 38 numbers 18 38 18 38 18 38 18 38 18 38 x x xx P(Winning) = = 0.02 (2d.p.)

8. 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 calculate the probability of independent events. What grade are we working at?

9. Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? PLENARY ACTIVITY – EXAM QUESTION (GRADE B) INDEPENDENT EVENTS Sam has two bags of marbles. Bag A contains 9 red marbles and 6 green marbles. Bag B contains 3 red marbles and 7 green marbles. Sam rolls a fair six-sided dice once. If she rolls a six she takes a marble from bag A. If she does not roll a six she takes a marble from bag B. Calculate the probability that Sam chooses a red marble. (3 marks) BAG A BAG B P(6) = 6 1 Bag A P(Not 6) = 6 5 Bag B P(Red) =(Rolling a 6, Red from bag A) + (Not rolling a 6, Red from bag B) P(Red) = 6 1 15 9 X + 6 5 10 3 X P(Red) = 90 9 + 60 15 = 20 7

10. Draw your brain What have you learnt? In your brain, write or draw everything you can remember about accurately calculating the probability of 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?

11. . 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

12. 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