MW4

MW4

1. Probability

   • Properties of Probability
     • The probability of an event will be between zero and one (O ≤ P(A) ≥ 1)
     • The Probability of sample space will equal to one (P(S) = 1)
     • Probability of disjoint event will equal to zero (P(Ø) = 0)
     • For any event A, P(A) is the sum of the probabilities of all outcomes in A
   • Probability Rules
     • The Addition Rule: P(A or B) = P(A) + P(B) - P(A and B)
     • The Multiplication Rule: P (A and B) = P(A) * P(B|A) or P(B) * P(A|B)
     • The Complement Rule: P(not A) = 1 - P(A)

2. Experiment: is an activity in which there are at least two possible outcomes and the result cannot be predicted with certainty

3. Sample space: the sample space with notation S in an experiment is the list of all possible outcomes of the experiment

4. Event: is a collection of outcomes from an experiment that is from the sample space

5. Venn Diagram

   • Complement: an event that didn’t happen notation is Ac or A’
   • Union (S): The union of two sets is a new set that contains all of the elements that are in at least one of the two sets
   • Intersect (∩): the events that are common between two sets
   • Disjoint (∩): Disjoint are sets events that never occur at the same time

6. Counting rule: The Fundamental Counting Principle (also called the counting rule) is a way to figure out the number of outcomes in a probability problem.

7. Multiplication Rule: find the probability of two events happening at the same time by multiplying the number of outcomes in these events together.

8. permutation: finding the number of ways a particular set can be arranged, where the order of the arrangement matters

9. Combination: determining the number of possible arrangements in a collection of items where the order of the selection does not matter

10. Conditional Probability: The likelihood of an event or outcome occurring, based on the occurrence of a previous event or outcome.

11. Independence: Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event.

12. Disjoint Events. Two events, say A and B, are defined as being disjoint if the occurrence of one precludes the occurrence of the other (no common outcomes)