1. OR b) Find the probability that he wins only one game
a) Find the probability that he wins both games
a) P(W,W) = 0.16
b) P(Wins once) = = 0.48
P(W,W) = 0.4 x 0.4 = 0.16
0.6
P(W,N) = 0.4 x 0.6 = 0.24 OR
P(N,W) = 0.6 x 0.4 = 0.24
0.4
0.6
0.6
P(N,N) = 0.6 x 0.6 = 0.36

2. b) Find the probability that at least one is at school
a) Neither is at school
b) P(at least one A) = = 0.72
a) P(D,D) = 0.12
0.7
Attends
P(A,A) = 0.6 x 0.7 = 0.42 OR
Doesn’t Attend
P(A,D) = 0.6 x 0.3 = 0.18
0.3 OR
Attends
P(D,A) = 0.4 x 0.7 = 0.28
0.7
0.4
Doesn’t Attend
P(D,D) = 0.4 x 0.3 = 0.12
0.3

3. b) Find the probability that at least one is red
a) Find the probability that both discs are the same colour
THINK…
When you have an AT LEAST ONE question where you must consider THREE of the FOUR combined probabiltiies..
What would be another way to get the same answer?
a) P(same) = 𝟒 𝟗 + 𝟏 𝟗 = 𝟓 𝟗
b) P(at least one red)= 𝟒 𝟗 + 𝟐 𝟗 + 𝟐 𝟗 = 𝟖 𝟗
𝟔 𝟗
RED
P(R,R) = 𝟔 𝟗 x 𝟔 𝟗 = 𝟒 𝟗 OR
𝟔 𝟗
RED
𝟑 𝟗
P(R,W) = 𝟔 𝟗 x 𝟑 𝟗 = 𝟐 𝟗
WHITE OR OR
𝟔 𝟗
P(W,R) = 𝟑 𝟗 x 𝟔 𝟗 = 𝟐 𝟗
RED
1 – P(W,W)= 1− 𝟏 𝟗 = 𝟗 𝟗 − 𝟏 𝟗 = 𝟖 𝟗
𝟑 𝟗
WHITE
P(W,W) = 𝟑 𝟗 x 𝟑 𝟗 = 𝟏 𝟗
𝟑 𝟗
WHITE

4. P(N,N) = ? 𝟗 𝟓𝟎 P(only one piece) = 𝟔 𝟓𝟎 + 𝟐𝟏 𝟓𝟎 = 𝟐𝟕 𝟓𝟎
𝟕 𝟏𝟎
P(Y,Y) = 𝟐 𝟓 x 𝟕 𝟏𝟎 = 𝟏𝟒 𝟓𝟎
YES
𝟐 𝟓
YES
𝟑 𝟏𝟎
P(Y,N) = 𝟐 𝟓 x 𝟑 𝟏𝟎 = 𝟔 𝟓𝟎 NO OR
𝟕 𝟏𝟎
P(N,Y) = 𝟑 𝟓 x 𝟕 𝟏𝟎 = 𝟐𝟏 𝟓𝟎
YES
𝟑 𝟓 NO
P(N,N) = 𝟑 𝟓 x 𝟑 𝟏𝟎 = 𝟗 𝟓𝟎
𝟑 𝟏𝟎 NO

5. We’re DONE …for this year
Senior 3 Probability
Senior 2 Probability
Possibility Space Diagrams
Probability Tree Diagrams
Prepare your mini-whiteboards

6. If you throw two dice, what is the probability of getting a “double”?
6, 6
6, 5
6, 4
6, 3
6, 2
6, 1 6
5, 6
5, 5
5, 4
5, 3
5, 2
5, 1 5
4, 6
4, 5
4, 4
4, 3
4, 2
4, 1 4
3, 6
3, 5
3, 4
3, 3
3, 2
3, 1 3
2, 6
2, 5
2, 4
2, 3
2, 2
2, 1 2
1, 6
1, 5
1, 4
1, 3
1, 2
1, 1 1
Second Dice
First Dice

7. If you throw two dice, what is the probability of getting a “double”?
6, 6
6, 5
6, 4
6, 3
6, 2
6, 1 6
5, 6
5, 5
5, 4
5, 3
5, 2
5, 1 5
4, 6
4, 5
4, 4
4, 3
4, 2
4, 1 4
3, 6
3, 5
3, 4
3, 3
3, 2
3, 1 3
2, 6
2, 5
2, 4
2, 3
2, 2
2, 1 2
1, 6
1, 5
1, 4
1, 3
1, 2
1, 1 1
Second Dice
First Dice
6 out of the 36 possible outcomes are “doubles”, so the probability is 𝟔 𝟑𝟔 = 𝟏 𝟔

8. P(two different colours) = P(R,B) or P(B,R) = 𝟐 𝟗 + 𝟐 𝟗 = 𝟒 𝟗
Based on the following tree diagram what is the probability I pick 2 different colours?
P(two different colours) = P(R,B) or P(B,R) = 𝟐 𝟗 + 𝟐 𝟗 = 𝟒 𝟗

9. The Watsons regard one boy and one girl as the ideal family
The Watsons regard one boy and one girl as the ideal family. What is the chance of getting one boy and one girl in their planned family of two?
First Child
Second Child
Combined G B
P(G,G) = 0.5 x 0.5 = 0.25
0.5 G B
0.5
P(G,B) = 0.5 x 0.5 = 0.25
P(B,G) = 0.5 x 0.5 = 0.25
P(B,B) = 0.5 x 0.5 = 0.25
Total = 1.00
The probability of getting one of each is:
P(G,B) + P(B,G) = = 0.5

10. Use your table to find the probability of getting a score of 7
In a game, two fair spinners are spun and a score is found by adding the numbers obtained together.
Use your table to find the probability of getting a score of 7
Find the probability of getting a score of 4 or less
Spinner A b)
2 outcomes out of 16 give a score of 7 a) 1 2 3 4 2 3 4 5 3 4 5 6
Spinner B 4 5 6 7 c) 5 6 7 8
6 outcomes out of 16 give a score of 4 or less

11. Johnny has a 0. 4 chance of scoring from a free-kick and a 0
Johnny has a 0.4 chance of scoring from a free-kick and a 0.7 chance of scoring from a penalty
Freekick
Penalty
Score
P(scores both)
Score
Miss
P(scores one)
Score
Miss
Miss
P(scores neither)

12. Probability Revision Worksheet for Friday
Remember do it carefully, it will be assessed!