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GCSE: AQA Unit 1 [calculator allowed]
A Concise Course in GCSE Probability
Example 1 – probability tables (mutually exclusive outcomes)
A spinner is spun, and the probability of each outcome is
detailed in the table below
Colour 
Probability 
Red 
0.2 
Green 
0.5 
Blue 
0.12 
Yellow 
Missing 
a) To find the value of
the missing outcome we work out
This means
b) If you are asked to
find P(Red or Yellow) we work out
c) Suppose the spinner is
spun twice and you want to find the probability of TWO reds. In other words P(Red and a Red).
We work out
d) Suppose the spinner is
spun a total of 250
times and you want to find how many Green you would expect. We know P(Green)=0.5. So:
We work out
So we would expect 125 Green’s
Example 2 – Picking out People from a Group (Dependent events)
You are told there are 8 males and 4 females in a room. Two
people are picked out at random.
a) Find the probability
they are both Male
Think about this carefully.
·
When the first male is picked there are eight males out of 12.
·
Once he has been picked, there are now 7 males to choose out of
11

Male 
and 
Male 


P(M
and M) 



= 

b) Find the probability
one is a male and one is a female
This needs even more careful though.
Remember that after one person has been picked there are only 11 people left
·
A male can be picked (8
out of 12) followed by a female (4 out of 11.
·
The other option is that a female can be picked first (4 out of
12) followed by a male (8 out of 11)
Option 1 
Male 1st 
and 
Female 2nd 






= 

Option 2 
Female
1st 
And 
Male
2nd 








Example 3 – tree diagrams
Tree diagrams can be used to simplify complicated situations
Suppose Peter drives through two sets of traffic lights.
For the first set P(green)=0.6
For the second set P(green)=0.7
Find the probability he gets delayed by AT LEAST one of the
lights (in other words, he meets at least one red light)
Firstly, we can draw a tree diagram:
P(RR)=
0.4x0.3=0.12 P(RG)=
0.4x0.7=0.28 P(GR)=
0.6x0.3=0.18 P(GG)= 0.6x0.7=0.42 Second Set First Set
Now to answer the original question: Add up all the options
which have at least once Red Light