conditional probability given

Let A and B be any two events associated with a random experiment. The probability of occurrence of event A when the event B has already occurred is called the conditional probability of A when B is given and is denoted as P(A/B..

Let us consider the random experiment of throwing a die. Let A be the event of getting an odd number on the die. \ S = {1, 2, 3, 4, 5, 6} and A = {1, 3, 5} Let B = {2, 3, 4, 5, 6}. If, after the die is thrown, we are given the information, that the event B has occurred, then the prob..

An event is the outcome or a combination of outcomes of an experiment. In other words, an event is a subset of the sample space. Whenever an outcome satisfies the conditions, given in the event, we say that the event has occurred . The Types of Events are: S..

A decorative item dealer deals in only two items - wall hangings and artificial plants. He has 15,000 dollars to invest and a space to store all the most 80 pieces. A wall hanging costs him 300 dollars and an artificial plant 300 dollars. He can sell a wall hanging at a profit of 50 dollars and an..

There are mainly four steps in the mathematical formulation of linear programming problem as a mathematical model. We will discuss formulation of those problems which involve only two variables. 1. Identify the decision variables and assign symbols x and y to them. These decision variab..

Mathematical Formulation of Linear Programming Problems - There are mainly four steps in the mathematical formulation of linear programming problem as a mathematical model. We will discuss formulation of those problems which involve only two variables. Identify the decision variables and assign sym..

Introduction - From our earlier chapter we know that, in statistical experiments, if the events A and B are independent, then But suppose the two events are not independent, that is the occurrence of one depends on the occurrence of other, then how do we compute This can be explained by condit..

If a trial results in n-exhaustive, mutually exclusive and equally likely cases and m of them are favourable to the occurrence of an event A, then the probability of the happening of A, denoted by P(A), is given by: P(A) = m/n. Important terms are 1. Statistical or Empiri..

Probability of an Event - So far, we have introduced the sample of an experiment and used it to describe events. In this section, we introduce probabilities associated to the events. If a trial results in n-exhaustive, mutually exclusive and equally likely cases and m of them ar..

An experiment repeated under essentially homogeneous and similar conditions results in an outcome, which is unique or not unique but may be one of the several possible outcomes. When the result is unique then the experiment is called a 'deterministic' experime..