Probability Formulae (Edexcel A Level Maths): Revision Note

Probability Formulae

What is meant by probability formulae?

• If you have seen any of the other Revision Notes on probability, almost every one contains a formula

  • These however are often disguised in Venn diagrams, tree diagrams etc

  • Sometimes a diagram can be easier to use than a formula

• This Revision Note rounds up all these formulae and introduces one or two new ones

What probability formulae are there?

• Some formulae only apply under certain conditions

• The formulae for probability you should’ve encountered so far

  • for independent events,       (“AND”, intersection)

  • for mutually exclusive events,     (“OR”, union)

  •       (“NOT”, complement/prime/dash)

  •      or                       (“GIVEN THAT”)            This second version in particular is referred to as the MULTIPLICATION FORMULA (see diagram below)

  • For independent events, 

• All of the formulae above are given in the formulae booklet but some are “hidden”

  • e.g. The formulae booklet lists the addition formula

  • but it does not list the rearranged version of it

  • nor does it point out that if  and  are mutually exclusive then 

    • and so 

How do I solve problems using probability formulae?

• This is a combination of

  • Recognising the set notation used

  • Taking note of any independent or mutually exclusive events

  • Using an appropriate diagram (Venn, mini-Venn, tree, two-way table)

  • Converting worded questions into AND, OR, GIVEN THAT etc statements

  • Knowing when a formula could be used and using the formulae booklet to double-check and confirm

• In the majority of cases a diagram can be used – so if you do not like using the formulae or find them confusing

  • For events that happen in succession, use a tree diagram; Venn diagrams suit most other purposes but two-way tables can be easier to follow

  • Of course, a question may give or demand the use of a particular diagram