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

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