1. Probability Trees
L.O.
All pupils can construct and use probability trees for unconditional information

9. Probability Trees
L.O.
All pupils can construct and use probability trees for unconditional information

16. Probability Trees
L.O.
All pupils can construct and use probability trees for unconditional information

17. Plenary:

18. Probability Trees
L.O.
All pupils can construct and use probability trees for unconditional information

19. Conditional Probability
L.O.
All pupils can construct and use probability trees for unconditional information
All pupils can find conditional probabilities without using tree disgrams

20. Starter:
Conditional Probability →
AND → X
OR → + 20

21. Starter:
Conditional Probability →
AND → X
OR → + 21

22. Starter: EXAMPLE x P(Second ball black) = P(Black and Black) = = =
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 6 1
P(Second ball black) = 9 4 x 8 3 72 12
P(Black and Black) = = = 22

23. Conditional Probability
L.O.
All pupils can construct and use probability trees for unconditional information
All pupils can find conditional probabilities without using tree disgrams

24. Main: CONDITONAL PROBABILITY TASK 1) 2) 3) 4) 5) P(W,B) =
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)
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)? 5)
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?
P(W,B) = 24

25. Main: CONDITONAL PROBABILITY EXTENSION 1) 2) 3) = = = = 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 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? = = = = 2) 3) 1 25

26. Mini-Plenary:
There are 13 teachers in the Mathematics Department in a 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?
First Pick
Second Pick
Third Pick
Fourth Pick
Fifth Pick 5 13 4 12 3 11 2 10 1 9 x x x x
120
154440 1
1287 26

27. Conditional Probability
L.O.
All pupils can construct and use probability trees for unconditional information
All pupils can find conditional probabilities without using tree disgrams

28. Plenary:
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.
TOTAL = 50
P(Adult Male, Adult Male) +
P(Adult Female, Adult Female) 21 50 20 49 14 50 13 49 x x + 6 35 13
175 + 43
175
(4 marks) 28

29. Conditional Probability
L.O.
All pupils can construct and use probability trees for unconditional information
All pupils can find conditional probabilities without using tree disgrams