Dr. Omar Al Jadaan Probability

Simple Probability Possibilities and Outcomes Expressed in the form of a fraction A/B Where A is the occurrence B is possible no. of outcomes Represented in the form: P(x) Example: six-sided dice Odd Number Even Number Less then a value

Set Notation Using set notation to show a group E.g.. Number set {1,2,3,4,5,6,7,8,9} AND( ∩ ), OR(  ) and NOT(‘) Venn diagrams

Exercise 1 Twenty 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) A multiple of 4 b) Even c) Greater then 15 d) Divisible by 5 e) Not a multiple of 6

Sum & Product Law Possibility Spaces Use of a diagram to prove the occurrence of the outcome of 2 different trials to happen Ego. Six-sided dice and coin toss Independent Events Outcome of one trail has not bearing on the outcome of the other trial Formula: P(A ∩ B) = P(A) x P(B)

Sum & Product Law Mutually Exclusive Events When the occurrence of one event automatically excludes the possibility of the other occurring. Either – Or Formula: P(A  B) = P(A) + P(B) Ego. Card selecting either a diamond of A of spades Not 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 happened

Conditional Probability We 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