Probability

Probability

  • Probability is a way of quantifying the likelihood that an event will occur.
  • An event’s probability is a number between 0 and 1, where 0 signifies an impossible event, and 1 signifies a certain event.
  • The sample space of an experiment is the set of all possible outcomes.
  • The sum of probabilities of all outcomes in a sample space is 1.

Fundamental Counting Principle

  • The Fundamental Counting Principle helps determine the total number of possible outcomes where there are multiple events.
  • If there are m ways to do one thing and n ways to do another, then there are m × n ways of doing both.

Independent and Dependent Events

  • Two events A and B are independent if the occurrence of A does not affect the probability of B, and vice versa.
  • If the occurrence of one event affects the occurrence of another, these events are dependent.

Conditional Probability

  • The probability that an event A occurs, given that event B has occurred, is referred to as conditional probability.

Disjoint Events and Intersection of Events

  • Two events are disjoint or mutually exclusive if they cannot both occur at the same time.
  • The intersection of two events A and B (denoted A ∩ B) is the set of outcomes that belongs to both A and B. For disjoint events, A ∩ B = ∅.

Addition Rule and Multiplication Rule

  • The Addition Rule is used for the probability that event A or B occurs, it is P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
  • The Multiplication Rule is used for the probability that events A and B both occur, it is P(A ∩ B) = P(A)P(B A) for dependent events, and P(A ∩ B) = P(A)P(B) for independent events.