Which ones are you using?

1. Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager Real life cross/curricular links? Where are we in our journey? Which ones are you using? PLT Skills LESSON OBJECTIVES Always aim high! We are learning to: • Enhance Mathematical basic skills knowledge. (Which PLT skills?) • Accurately calculate the probability of independent events. (Grades B-A) AUTHOR www.mistrymaths.co.uk

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

3. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager STARTER PLT Skills TASK Find the median of: 3, 6, 9, 12 2) x - 2x When x = -3 2 Expand -5(-4x - 3) 1) 3) 20x + 15 = 7.5 = 2 = 15 = (-3) -2 X -3 4) 2 Calculate 11 Find the LCM of 8 and 4. 5) 6) 11 x 11 = = 121 = 5 = 8 Simplify: 8e + 6y – 9e + 7y Solve: 6(x + 8) = 60 50% of 40miles 7) 8) 9) 20miles = -e = 60 6x + 48 + 13y = EXTENSION = 12 6x x = 2 9m Calculate the area of the trapezium 2m 2 Area = Area = 20m Area = (a + b)h (9 + 11)2 11m

4. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager INDEPENDENT EVENTS PLT Skills Independent Events → OR → + AND → X EXAMPLE 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? (b) Hits target only once (c) Hits target at least once (a) Hits target both times P(Hits target once only) P(Hits both times) P(Hits at least once) This is the same as This is the same as This is the same as P(1st hits 2nd hits) and P(1st hits,2nd misses 1st misses,2nd hits) or 3 6 3 3 1 16 16 16 8 16 x x x + + Worked out in (a) Worked out in (b) P(Hits both times) = P(Hits target once only) = + P(Hits target once only) = = +

5. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager INDEPENDENT EVENTS 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)? 2) 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)? 3) A dice is thrown twice. What is the probability that both scores are: (a) even (b) one even and one odd (in any order)? 4) I throw a dice three times. What is the probability of getting three sixes? 5) 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)? 6) 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. = = 0.48

6. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager INDEPENDENT EVENTS PLT Skills EXTENSION (GRADE A) 1) 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? = 0.336 = 0.452 = 0.024 2) 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? = 0.19 = 0.77 = 0.512 3) What is the probability of rolling the same number on a dice five times in a row? 4) Explain why picking a red card from a pack of cards and picking a King from a pack of cards are not independent events. Red cards can also be kings so it becomes dependent

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

8. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager • LINK BACK TO OBJECTIVES • Accurately calculate the probability of independent events. What grade are we working at? DISCOVERY PLT Skills

9. Which ones are you using? Team Worker Creative Thinker Effective Participator Independent Enquirer Reflective Learner Self Manager INDEPENDENT EVENTS PLT Skills PLENARY ACTIVITY – EXAM QUESTION (GRADE B) 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. Bag A Bag B 7 15 9 3 9 1 5 1 5 20 60 6 6 90 15 10 6 6 BAG B BAG A + (Not rolling a 6, Red from bag B) P(Red) = (Rolling a 6, Red from bag A) + P(Red) = X X + = P(Red) = (3 marks) P(Not 6) = P(6) =

10. What grade are we working at? Where are we in our journey? What have you learnt? Draw your brain 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.

11. Team Worker Positive Thinker Creative Entrepreneur Independent Learner Reflective Learner Responsible Citizen SELF ASSESSMENT Enterprise Skills Which ones are you using? Plenary Activity How well do you understand the task? . I fully understand I don’t understand I nearly understand www.mistrymaths.co.uk

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