Probability Rules, Definitions and Notation

Probability: Chance of so happening determine by one of the following:

  1. Theoretical: Proportion of equally likel outcomes. EX: (Rolling a Dice 1/6)

  2. Law of Large Numbers: Proportion of outcomes observed in the long run. EX: (Roll Dice 50 times) ( Probabiliy of a student getting an A is .25)

  3. Subjective: Likelihood assessed Subjectively EX: (Probability of winning sports game is .70)

Notation:

  • P(A): Probability of event A occurring

  • P(A') or P(¬A): Probability of event A not occurring (complement)

  • P(A | B): Conditional probability of event A given event B

  • P(A and B): Joint probability of events A and B occurring together

  • P(A or B): Probability of either event A or event B occurring (inclusion-exclusion principle).

Use Capital letters to denote events in probability:

  • H= getting a heart in a Deck of Cards

Use  to denote probability of event:

  • P (   )  to P (H)

Use to denote the event that an event A does not occur.

  • P (not A)

Permissible Probability Rule: The probability of an impossible event is 0, the probability of a certain event is 1, and all probabilities must be between 0 and 1.