1. Possibility Space Diagrams
What do you remember?

2. L.O. To be able to draw a possibility space diagram and find probabilities from it
By the end of the lesson we will be able to:
identify whether the outcomes are a list type or number type
correctly draw and label the possibility space diagram
answer probability questions about the combined outcomes
give answers in their lowest terms

3. Possibility Space Diagrams
In a possibility space diagram we list all the possible outcomes of two events happening together and we use them to find the probability of the combined outcomes!
EVENT A
Possible outcomes of Event A
E V E N T B
Possible outcomes of
Event B
The COMBINED
Possible Outcomes

4. John has shirts in blue, white and green
John has shirts in blue, white and green. He has trousers in blue and purple. Draw a possibility space diagram for all the possible outcomes of John’s clothes.
What is the probability that when John dresses in the dark he is wearing:
a) Blue and White? P(B,W)=
b) Only blue? P(B,B)=
c) Purple trousers? P(P trousers)=

5. John’s Clothes Shirts Trousers BLUE WHITE GREEN (B,B) (B,W) (B,G)
PURPLE
(P,B)
(P,W)
(P,G)
Trousers
P(B,B)= 𝟏 𝟔
P(B,W) = 𝟏 𝟔
P(P trousers)= 𝟑 𝟔 = 𝟏 𝟐

6. Three cards are numbered 1,3 and 4
Three cards are numbered 1,3 and 4. Three discs are numbered 21, 4 and 5. 21 4 5 1 3 4
A game consists of picking one card at random and one disc at random. The number on the card is subtracted from the number on the disc.
Draw a possibility space diagram
What is the probability of scoring 1
What is the probability of scoring 4 or more?
What is the probability of getting an even score?

7. Cards and Discs Discs Cards 21 4 5 1 20 3 18 2 17 P(1) = 𝟐 𝟗
Cards
P(1) = 𝟐 𝟗
P(4 or more) = 𝟒 𝟗
P(even) = 𝟓 𝟗

8. A B&B has sheets in the colours pink, white and blue and pillow cases in the colours pink, white, yellow and blue. Draw a possibility space diagram for all possible combinations.
What is the probability of randomly picking from the drawer: a) a white sheet and a pink pillowcase? P(W,P)= b) a white pillowcase? P(white pillow)= c) a bed in one colour? P(one colour)=

9. Bed & Breakfast, sheets & cases
Pillow Cases
PINK
YELLOW
BLUE
WHITE
(B,P)
(B,Y)
(B,B)
(B,W)
(P,P)
(P,Y)
(P,B)
(P,W)
(W,P)
(W,Y)
(W,B)
(W,W)
Sheets
P(W,P)= 𝟏 𝟏𝟐
P(white pillow)= 𝟑 𝟏𝟐 = 𝟏 𝟒
P(one colour)= 𝟑 𝟏𝟐 = 𝟏 𝟒

10. Two spinners A and B are spun and the scores are added together
a) Draw a sample space diagram b) What is the probability of scoring a total of 2? c) What is the probability of an odd total? d)What is the probability of a total that is prime?

11. Spinners A and B 1 2 3 P(2)= 𝟑 𝟏𝟖 = 𝟏 𝟔 P(odd)= 𝟖 𝟏𝟖 = 𝟒 𝟗
Spinner A 1 2 3 4 5 6
Spinner B
P(2)= 𝟑 𝟏𝟖 = 𝟏 𝟔
P(odd)= 𝟖 𝟏𝟖 = 𝟒 𝟗
P(prime)= 𝟏𝟏 𝟏𝟖

12. L.O. To be able to draw a possibility space diagram and find probabilities from it
By the end of the lesson we will be able to:
identify whether the outcomes are a list type or number type
correctly draw and label the possibility space diagram
answer probability questions about the combined outcomes
give answers in their lowest terms

13. A machine offers Coffee(C), Tea(T) or Espresso(E)
Macy and Gracy each buy a drink from this machine:
Draw a possibility space diagram to show all possible outcomes
What is the probability that they both buy the same drink?
Find the probability that at least one of them buys a coffee

14. Coffee Machine P(same drink)= 𝟑 𝟗 = 𝟏 𝟑 P(one coffee)= 𝟓 𝟗
Macy’s Drink
Coffee
Tea
Espresso
(C,C)
(C,T)
(C,E)
(T,C)
(T,T)
(T,E)
(E,C)
(E,T)
(E,E)
Gracy’s
Drink
P(same drink)= 𝟑 𝟗 = 𝟏 𝟑
P(one coffee)= 𝟓 𝟗

15. Sue has three cards numbered 2,3 and 4
Sue has three cards numbered 2,3 and 4. Danny has three cards numbered 4,5 and 6.
They both pick a card at random, then multiply the numbers to obtain a score.
Draw a possibility space diagram to show the combined outcomes
Find the probability that the score is a multiple of 4
Find the probability that the score is greater than 15

16. Sue & Danny’s cards
Sue’s cards 2 3 4 8 12 16 5 10 15 20 6 18 24
Danny’s
cards
P(multiple of 4)= 𝟔 𝟗 = 𝟐 𝟑
P(> 15)= 𝟒 𝟗