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• Probability is used to describe the phenomenon of chance or randomness of events to occur.
• Types of Probability

  1. subjective probability
  2. objective probability
• types of SUBJECTIVE PROBABILITY

  1. OPINION POLLS
  2. JUDGEMENT OF EXPERT
  3. DELPHI METHODS
• Simple Event: Probability of getting a Head (H) when a coin is tossed; Probability of getting 1 when a die is thrown.
• Basic Properties of Probabilities

  Property 1: The probability, P, of any event or state of nature occurring lies

  between greater than or equal to 0 or 0% and less than or equal to 1 or 100%.

  Property 2: The probability of an event will not be less than 0 because it is not

  possible (impossible) or can never occur.

  Property 3: The probability of an event will not be more than 1 because

  1 is certain that something will happen (sure event).
• Tree diagram is a device consisting of line segments beginning a starting point and also from the outcome point.
• Disjoint events(mutually exclusive events):

  Two events are mutually exclusive events if they cannot occur at the same time
• 
  

  If event A occurs affect the probability of event B occurring, the two events are dependent events.
• Permutation is a counting technique which refers to the arrangement (or ordering) of a set of objects, from first to last, where the order in which the objects

  are selected does matter.
• Combination is a selection of objects from a collection in any order as oppose to

  permutations which deal with the ordered arrangements of objects.
• Probability does not deal with guarantees, but with the likelihood of

  an occurrence of an event.
• If we understand how to calculate probabilities, we can make thoughtful

  decisions about random and unpredictable situations where multiple outcomes are possible.
• If eventAoccurs does not affect the probability of event B occurring, the two events are independent events.
• Compound Event: When two coins are tossed, probability of getting a Head (H) in the first toss and getting a Tail (T) in the second toss.
• RULES OF PROBABILITY: General multiplication rule

  two events are dependent if the occurrence of one event does affect the likelihood that the other event will happen.
• RULES OF PROBABILITY: Special Multiplication Rule

  two events are independent if the occurrence or nonoccurrence of one of the events does not affect the likelihood that the other event will occur.
• Formula for independent events: P(A and B) = P(A) * P(B)
• GENERAL MULTIPLATION RULE

  P(A and B) =P(A) * P(B | A)
• GENERAL MULTIPLATION RULE

  another form of conditional probability
• Combination Selection Rules: Each object can be selected only once; this implies that you are not allowed any repeat numbers.
• Combination formula

  A) C

  B) n!

  C) r!(n-r)!

  
• Permutation: some items consist of look-alike/duplicate and rest are all different
• In permutation, n different objects taken r at a time (where r is a subset of n), an event cannot repeat
• Permutation Formula

  A) P

  B) n!

  C) (n-r)!

  
• SUBJECTIVE - Based on past experiences and judgment of the person that it would simply determine the possible occurrences of events
• OBJECTIVE - Empirical or experimental probability. Using past data to determining the likeliness of the event to occur.