1. ©G Dear 2010 – Not to be sold/Free to use
Applied Mathematic
(Preliminary General 1)
Probability
Probability Trees
Stage 6 - Year 11
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©G Dear 2010 – Not to be sold/Free to use

2. Probability Trees
If a probability experiment has more than one stage then a probability tree could/should be used. H H T H H T T H H T T H T T

3. List all the possibilities of tossing 3 coins.
Probability Trees
List all the possibilities of tossing 3 coins.  1 8 
P(HHH) =  H T 3 8 
P(HHT) =  4 8 1 2 
P(TT) = =  
S={HHH,
HHT,
HTH,
HTT,
THH,
THT,
TTH,
TTT}
n(S) = 8

4. Rules Probability Trees 1. Multiply along branches. H
2. Add branches together.

5.     Probability Trees
There are 5 red and 3 blue counters in a bag. Two counters are chosen, no replacement.  5 8 4 7 = 20 56 = 5 8 x 4 7
P(RR) = R B 5 8 R B  3 8 2 7 = 6 56 = 3 8 3 7 x
P(BB) =  5 7 R B 5 8 3 7 3 8 5 7 x + x
P(RB) = 3 8  2 7 = 30 56 = 15 28

6.     Probability Trees
There are 5 red and 3 blue counters in a bag. Two counters are chosen, with replacement.  5 8 5 8 = 25 64 x 5 8
P(RR) = R B 5 8 R B  3 8 3 8 = 9 64 3 8 x
P(BB) =  5 8 R B 5 8 3 8 3 8 5 8 x + x
P(RB) = 3 8  3 8 = 30 64 = 15 32

7.     Probability Trees
Three die are rolled. What is the probability of rolling at least two sixes?  1 6 1 6 1 6 6 N x x 1 6
1/6
P(66) =  
5/6 1 6 5 6 1 6 1 6 + x x 5 6
1/6
5/6  5 6 1 6 1 6 1 6 + x x
1/6 5 6
5/6 5 6 1 6 1 6 5 6 + x x
1/6
5/6 = 16
216 = 2 27