conditional probabilities

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 probability..

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..

Introduction - 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 conditional probability. Baye's theorem is named after the British mathematician Thomas Bayes who publishe..

From the formula of conditional probabilities, we have Equation (2) and equation (3) are known as multiplication rules of probability for any two events A and B of the same sample spa..

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 experiment . Any experim..

In this chapter we have studied the method of evaluating probabilities of events relating to independent events and conditional events. We have also studied about random variables and their probability distributions, namely binomial distribution and Poisson distributio..

Multiplication Rule of Probability - We have already proved that if two events A and B from a sample S of a random experiment are mutually exclusive, then In this section, we examine whether such a rule exists, if ' ' is replaced by ' ' and '+' is replaced by 'x' in the above addition rul..

We have already proved that if two events A and B from a sample S of a random experiment are mutually exclusive, then In this section, we examine whether such a rule exists, if ' ' is replaced by ' ' and '+' is replaced by 'x' in the above addition rule. If it does exist, what are the particular ..

Random Experiment and Sample Space - 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' ..