Probability and Probability Distribution

Probability and Probability Distribution

1. Random Experiment: An experiment where all the elements of a sample of the universe are selected aritrarily

2. Random: This describes a situation where any element has the same chance of being selected in the sample of the universe.

3. Sample Space: It is also known as event space. It is a subset of a set of elementary events that occurs in the probability calculation.

4. Event: It is an incident in whose realization chance intervenes.

5. Probability of an event: From a practical point of view, we interpret the fraction of the population that produces the event as the probability of e.

6. Mutually exclusive events: We say two events A and B are mutually exclusive if the event A ∩ B has no sample point (is empty).

   • Independent events: Two events A and B are independent if: P(B|A) = P(A) or P(B)
   • Complementary Events: It is obtained by the complement of the unit; this menas that the complementary of the event.

7. Addition Rule

   • P (A U B) = P(A) + P(B) - P(A ∩ B)

8. Multiplication Rule

   • P (A ∩ B) = P(A) P(B)

9. Basic Counting Principle: if an activity can be done in n1 different days and a second activity can be done in n2 different ways, and a kth activity can be done nk ways; they can be done by multiplying them all.

   • Combination Vs. Premutation: in premutation order or arrangements matter and in combination order of arrangement does not matter.