Probability

  • Subjective Probability

    A person may some confidence or belief regarding the occurrence of some event, Say A. The numerical measure of this confidence is called the subjective probability of the occurrence of A. This probability is based on the experience, intelligence and knowledge of the person who determining the probability in some situation. For example, we may […]

  • Definition of Probability

    Probability is something strange and it has been defined in different manners. We can define probability in objective or subjective manner. Let us first use objective approach to define probability. The Classical Definition of Probability: This definition is for equally likely outcomes. If an experiment can produced mutually exclusive and equally likely outcomes out of […]

  • Relative Frequency

    The term relative frequency is used for the ratio of the observed frequency of some outcome and the total frequency of the random experiment. Suppose a random experiment is repeated times and some outcomes is observed times, then the ratio is called the relative frequency of the outcome which has been observed times. Some examples […]

  • Reduced Sample Space

    Sometimes the sample space is reduced in size and is called reduced sample space. The symbol may be used for a reduced sample space. Suppose s die has been thrown and we have been informed that the experiment has produced an even face. This type of information is called the additional information. Thus the reduced […]

  • Exhaustive and Complementary Events

    Exhaustive Events: When a sample space is partitioned into some mutually exclusive events such that their union is the sample space itself then the events are called exhaustive events or collectively events. Suppose a die is tossed and the sample space is                         Let                         Hence the events and are mutually exclusive because […]

  • Not Mutually Exclusive Events

    Two events are called not mutually exclusive if they have al least one outcome common between them. If the two events and are not mutually exclusive events, then .  Similarly, and are not mutually exclusive events if . Thus they must have at least one common point between them. Consider a sample space: Let    […]

  • Mutually Exclusive Events

    Two events are called mutually exclusive or disjoint if they do not have any outcome common between them. If the two events and are mutually exclusive, then (null set). For three mutually exclusive events and , we have . Suppose there is a sample space as: Let    and   Here . Thus and are mutually […]

  • Equally Likely Outcomes

    The outcomes of a sample space are called equally likely if all of them have the same chance of occurrence. It is very difficult to decide whether or not the outcomes are equally likely. But in this tutorial we shall assume in most of the experiments that the outcomes are equally likely. We shall apply […]

  • Event of Probability

    Any part of the sample space is called an even of a probability. An event may contain one or more than one outcomes. When an event consists of a single outcome (sample points), it is called a simple event. An event which has two or more outcomes is called a compound event. The sample points […]

  • Sample Space

    A complete list of all possible outcomes of a random experiment is called sample space or possibility space and is denoted by . Each outcome is called element of the sample space. A sample space may be containing any number of outcomes. If it contains finite number of outcomes, it is called finite or discrete […]

  • Random Experiment

    The word experiment or random experiment is used for a situation of uncertainty about which we want to have some observations. The actual results of the uncertain situation is called outcome or sample point. In the random experiment, nothing can say with certain about the outcome. An experiment may consist of one or more observations. […]

  • Introduction to Probability

    We live in the world of uncertainties. Man is surrounded by situations which are not fully under his control. The nature commands these situations. A person on a road does not know whether or not he will reach his destination safely. A patient in the hospital is never sure about his survival after a delicate […]