Probability

Dr. Omar Al Jadaan

ProbabilitySimple ProbabilityPossibilities and OutcomesExpressed in the form of a fraction A/BWhere A is the occurrenceB is possible no. of outcomesRepresented in the form: P(x)Example: six-sided diceOdd NumberEven NumberLess then a value

Set NotationUsing set notation to show a groupE.g.. Number set {1,2,3,4,5,6,7,8,9}AND(), OR() and NOT()Venn diagrams

Exercise 1Twenty cards are numbered 1 to 20. One card is then taken at random. What is the probability that the number on the card is:A multiple of 4EvenGreater then 15Divisible by 5Not a multiple of 6Sum & Product LawPossibility SpacesUse of a diagram to prove the occurrence of the outcome of 2 different trials to happenEgo. Six-sided dice and coin tossIndependent EventsOutcome of one trail has not bearing on the outcome of the other trialFormula: P(A B) = P(A) x P(B)Sum & Product LawMutually Exclusive EventsWhen the occurrence of one event automatically excludes the possibility of the other occurring.Either OrFormula: P(A B) = P(A) + P(B)

Ego. Card selecting either a diamond of A of spadesNot mutually exclusive event (e.g.. Diamond or Queens)Tree Diagrams

Formula of Dependent Events:P(A B) = P(A) x P(B|A)Where P(B|A) is the occurring of B after A has happenedConditional ProbabilityWe know that:P(A B) = P(A) x P(B|A)

Another way to represent it:P(B|A) = P(A B) / P(A)Example

Example Tree Diagram