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We are learning to: - Enhance Mathematical basic skills knowledge. (Which PLT skills?) -Accurately calculate conditional probability without tree diagrams.

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Presentation on theme: "We are learning to: - Enhance Mathematical basic skills knowledge. (Which PLT skills?) -Accurately calculate conditional probability without tree diagrams."— Presentation transcript:

1 We are learning to: - Enhance Mathematical basic skills knowledge. (Which PLT skills?) -Accurately calculate conditional probability without tree diagrams. (Grades A-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 TASK 1) 2) 3) 4) x - 2x + 1 When x = -1 Expand: (x + 2)(x + 5) Factorise: 5) Simplify the surd: 20 6) Write as a fraction: 2 Solve: 7x – 5 = 5x + 28 = EXTENSION x + 7x + 12 2 Write: 75400000 In standard form 7 x 2 + 2x + 5x+ 10 = x 2 + 7x + 10 = (-1) 2 -2 x -1 + 1 = 1+ 2 + 1 4 = = ( )( ) x x +x + 4+ 3 7.54 x 10 7 4 x 5 = 2 5 = 7 1 = = - 5 2 - 5 = 28 + 5 2= 33 2= ÷ 2 = 16.5

4 CONDITONAL PROBABILITY Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXAMPLE Conditional Probability → AND → X OR → + A bag contains nine balls, of which five are white and four are black. A ball is taken out and not replaced. Another is then taken out. If the first ball removed is black, what is the probability that: (a) the second ball will be black (b) both balls will be black? First ball removed → What is left? P(Second ball black) = 8 3 First Pick Black 9 4 Second Pick Black 8 3 P(Black and Black) = 9 4 x 8 3 = 72 12 = 6 1

5 Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills TASK (GRADE A) 1) A bag contains 7 beads. Four beads are green and the rest orange. A bead is taken from the bag at random and not replaced. What is the probability of: (a) two greens (b) two oranges? Jonjo draws a card from a pack of cards, does not replace 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)? 2) 4) 5) CONDITONAL PROBABILITY A bag contains 8 marbles. 6 marbles are blue, 2 are red and the rest black. A marble is taken from the bag at random and not replaced. What is the probability of: (a) two blues (b) two reds (c) Same colour twice? A bag contains 9 counters. Two-thirds of the counters of purple and the rest yellow. A counter is taken from the bag at random and not replaced. What is the probability of: (a) two purples (b) two yellows (c) One of each in any order? 3) There are five white eggs and one brown egg in an egg box. Kate decides to make a two egg omelette. She takes each egg from the box without looking at its colour. (a) What is the probability that the first egg taken is brown? (b) If the first egg taken is brown, what is the probability that the second egg taken will be brown? (c) What is the probability that Kate gets an omelette made from: (i) two white eggs (ii) one white and one brown egg (iii) two brown eggs? 0 0

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) CONDITONAL PROBABILITY A box contains 10 red and 15 yellow balls. One is taken out and not replaced. Another is taken out. (a) If the first ball taken out is red, what is the probability that the second ball is: (i) red (ii) yellow? (b) If the first ball taken out is yellow, what is the probability that the second ball is: (i) red (ii) yellow? A fruit bowl contains six Granny Smith apples and eight Golden Delicious apples. Kevin takes two apples at random. (a) If the first apple is a Granny Smith, what is the probability that the second is: (i) a Granny Smith (ii) a Golden Delicious? (b) What is the probability that: (i) both are Granny Smiths (ii) both are Golden Delicious? Ann has a bargain box of tins. They are unlabelled but she knows that six tins contain soup and four contain peaches. (a) She opens two tins. What is the probability that: (i) they are both soup (ii) they are both peaches? (b) What is the probability that she has to open two tins before she gets a tin of peaches? (c) What is the probability that she has to open three tins before she gets a tin of peaches? (d) What is the probability that she will get a tin of soup if she opens five tins? 3) = = = = 1

7 Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? MINI-PLENARY ACTIVITY There are 13 teachers in the Mathematics Department in this school. 5 are male and 8 are female. If you were to place all their names in a hat, what is the probability of picking 5 male teachers in a row without replacing the names once they have been picked? CONDITONAL PROBABILITY 5 13 First Pick 4 12 Second Pick 3 11 Third Pick 2 10 Fourth Pick 1 9 Fifth Pick x x x x 120 154440 1 1287

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 conditional probability without tree diagrams. 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 A*) (4 marks) CONDITONAL PROBABILITY The types of people watching a film at a cinema are shown in the table. Two of these people are chosen at random to receive free cinema tickets. Calculate the probability that the two people are adults of the same gender. P(Adult Male, Adult Male) P(Adult Female, Adult Female) + TOTAL = 50 21 50 20 49 x + 14 50 13 49 x 6 35 + 13 175 43 175

10 Draw your brain What have you learnt? In your brain, write or draw everything you can remember about accurately calculating conditional probability without trees. 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 don’t 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

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