1. ©G Dear2009 – Not to be sold/Free to use
General Mathematic
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Probability Trees
Stage 6 - Year 12
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©G Dear2009 – Not to be sold/Free to use

2. Probability Trees We draw a marble from a bag that contains two 
green, a blue
and a red
marble. 1  2
Green 3  4 5 6 
P(Green,Even) = 6 24 1  2 1 =
and
roll
a die.
Green 3  4 4 5  6 1 2 3
What
is the
probability
of getting
a green and
an even number?
Blue 4 5 6 1 2 3
Red 4 5 6
End of
Slide

3. Probability Trees A better way Green Green 2 4 1 Blue 4 Blue 1 4 Red3 4 5 6
Green
Blue
Red 1 2
Odd
Green 2 4 1 2
Even 1 2
Odd 1 4
Blue 1 2
Even 1 4 1 2
Odd
Red 1 2
Even
End of
Slide

4. Multiply along the branches.
Probability Trees
Multiply along the branches.
Odd
Green
Blue
Red
Even 2 4 1
A better way 2
P(Green,Even) = 8 2 4 1 2 2 8 1
x = = 4
We draw a marble from a bag that contains two green, a blue and a red marble and roll a die.
What is the probability of getting a green and an even number?
End of
Slide

5. Multiply along the branches.
Probability Trees
What is the probability of a Green or Red and an Even Number?
Odd
Green
Blue
Red
Even 2 4 1
Multiply along the branches.
Add Branches together. 2 4 1 2 2 8
x =
P(G,R,Even) = 2 8 1 8 + 3 8 = 1 4 1 2 1 8
x =
End of
Slide

6. 6 6 Not 6 Not Not Probability Trees
A game requires a ‘Double-Six’ to start.
What is the probability of a ‘Double-Six’? 1 6 1 6 1 6 1 36 6 = X 1 6 6 5 6
Not 1 36
P(6,6) = 1 6 6 5 6
Not 5 6
Not
End of
Slide

7. What is the probability of a ‘Only One Six’?
Probability Trees
What is the probability of a ‘Only One Six’? 1 6 5 36 5 36 6
P(Only One Six) = + 1 6 6 10 36 5 6 1 6 5 6 5 36 =
Not = X 5 18 = 1 6 5 6 1 6 5 36 6 = X 5 6
Not 5 6
Not
End of
Slide

8. Probability Trees with Replacement
A standard pack of cards has 52 cards.
13 
13 
13 
13 
Two Cards are chosen and replaced.
What is the probability of 2 red cards?
Red. 26 52 26 52 26 52
P(Red,Red) = x
Red. 26 52 1 4 26 52 =
Black
Red. 26 52 26 52
Black 26 52
End of
Slide
Black

9. Trees -Without Replacement
A standard pack of cards has 52 cards.
13 
13 
13 
13 
Two Cards are chosen and NOT replaced.
What is the probability of 2 red cards?
Red. 25 51 26 52 25 51
P(Red,Red) = x
Red. 26 52 25
102 26 51 =
Black
Red. 26 51 26 52
Black 25 51
End of
Show
Black