Probability

Probability

1. Basic concepts

   • Outcomes: possible results
     • Example: The results of throwing a dice
   • Sample space: all outcomes
     • Ex: 1,2,3,4,5,6 (when throwing a dice)
   • Event: subgroup of sample space
     • Ex: Getting a 4 when throwing a dice
   • Experiment: observation, measurement.
     • Ex: Throwing a dice 4 times to observe the results obtained
   • Odds
     • favorable or not favorable to an event
     • Favor: a to b Against: b to a

2. Formulas

   • Theoretical
     • • All the results must be equiprobable.
   • Empirical
     • • When results are not equiprobable

3. Events involving "not" and "or"

   • Addition rule of probability P(A∪B)=P(A)+P(B)-P(A∩B)
     • For mutually exclusive events P(A∪B)=P(A)+P(B)
       • Mutually exclusive events are the ones that do not interfere with each other
   • Probability of the complement P(E' )=1-P(E)
     • The complement consists of all outcomes that are not the event.

4. Properties

   • Probability value 0≤P(E) ≤1
   • Impossible events P(∅)=O
   • Certain event P(s)=1

5. Events involving "and"

   • Conditional probability formula
   • Multiplication rule of probability
     • For independent events
       • Events are independent if P(B|A)=P(B)
     • For any two events P(A∩B)=P(A)×P(B|A)

6. Venn Diagrams

   • Complement
   • Intersection
   • Difference
   • Union

Images and files in the map