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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












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







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


Female 2nd





Option 2

Female 1st


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