LESSON OBJECTIVES We are learning to: Accurately calculate conditional probability without tree diagrams. (Grades A/A*)

STARTER TASK Expand: (x + 2)(x + 5) x - 2x + 1 When x = -1 Factorise: 1) Expand: (x + 2)(x + 5) 2) x - 2x + 1 When x = -1 2 3) Factorise: x + 7x + 12 2 4) Write: 75400000 In standard form 5) Simplify the surd: 20 6) Write as a fraction: 7 -1 EXTENSION Solve: 7x – 5 = 5x + 28 2

CONDITONAL PROBABILITY Conditional Probability → OR → + AND → X EXAMPLE 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 Pick Black First ball removed → 9 4 What is left? Second Pick Black 8 3 8 3 P(Second ball black) = 9 4 x 8 3 72 12 6 1 P(Black and Black) = = = 3

CONDITONAL PROBABILITY 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? 2) 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? 3) 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? 4) There are five white eggs and one brown egg in an egg box. Kate decides to make a two egg omelets. She takes each egg from the box without looking at its colour. 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? P(W,B) = 4

CONDITONAL PROBABILITY EXTENSION (GRADE A*) 1) 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: 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 not labelled 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? 2) 3) 5

MINI-PLENARY ACTIVITY CONDITONAL PROBABILITY 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? 6

PLENARY ACTIVITY – EXAM QUESTION (GRADE A*) CONDITONAL PROBABILITY PLENARY ACTIVITY – EXAM QUESTION (GRADE A*) 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. 7