Many businesses apply the understanding of uncertainty and probability in their business decision practices. Probability models can greatly help businesses in optimizing their policies and making safe decisions. Though complex, these probability methods can increase the profitability and success of a business.

You can calculate the probability that an event will happen by dividing the number of ways that the event can happen by the number of total possibilities. Probability can help you to make better decisions, such as deciding whether or not to play a game where the outcome may not be immediately obvious.

Probability is the branch of mathematics concerned with the assessment and analysis of uncertainty. The theory of probability provides the means to rationally model, analyze and solve problems where future events cannot be foreseen with certitude. Thus, probability theory is indispensable for rational decision making.

Probability provides information about the likelihood that something will happen. Meteorologists, for instance, use weather patterns to predict the probability of rain. In epidemiology, probability theory is used to understand the relationship between exposures and the risk of health effects.

Getting a 3 on the toss of a die and getting a 5 on the toss of a die are equally likely events, since the probabilities of each event are equal. Getting a 1, 2 or 3 on the toss of a die and getting a 4, 5 or 6 on the toss of a die are equally likely events, since the probabilities of each event are equal.

Impossible Event. An impossible event is an event that cannot happen. E is an impossible event if and only if P(E) = 0. In flipping a coin once, an impossible event would be getting BOTH a head AND a tail.

The probability of an event is a number describing the chance that the event will happen. An event that is certain to happen has a probability of 1. An event that cannot possibly happen has a probability of zero. If there is a chance that an event will happen, then its probability is between zero and 1.

The event that is most likely to happen is called Likely Event.

1 Answer. The sum of the probabilities in a probability distribution is always 1. A probability distribution is a collection of probabilities that defines the likelihood of observing all of the various outcomes of an event or experiment.

The outcomes of a sample space are called equally likely if all of them have the same chance of occurring.

Complete step-by-step answer: Example: – choosing a heart and choosing a spade from a deck of cards are the equally likely events. This experiment has equally likely outcomes. You can see the probabilities for all are the same so there are equally likely outcomes.

When a sample space consists of outcomes that don’t have an equal chance of occurrence, then the resultant outcomes are said to be not equally likely outcomes.

The probability of an impossible event is 0 and the probability of a certain event is 1. The range of possible probabilities is: 0 ≤ P ( A ) ≤ 1 . It is not possible to have a probability less than 0 or greater than 1.

Therefore (iii) is the only experiment that does not have equally likely outcomes.

The sample space of a random experiment is the collection of all possible outcomes. An event associated with a random experiment is a subset of the sample space. The probability of any outcome is a number between 0 and 1.

Thus we can say, an experiment is called a Random Experiment if it satisfies two conditions: All the possible results of the random experiment are called outcomes. If chances of occurrence of all the outcomes are equal then they are termed as Equally Likely Outcomes.

The sample space is the set of all possible outcomes of a random experiment, we will denote it by S . An event is a subset of the sample space (any set of outcomes of the random experiment). The certain event, S , always occurs. The null (impossible) event, ∅ , does never occur.

Definition : A random experiment is an experiment or a process for which the outcome cannot be predicted with certainty. Definition : The sample space (denoted S) of a random experiment is the set of all possible outcomes.

An experiment is said to be random if it has more than one possible outcome, and deterministic if it has only one. A random experiment that has exactly two (mutually exclusive) possible outcomes is known as a Bernoulli trial.

Two events associated with a random experiment are said to be mutually exclusive if both cannot occur together in the same trial. Mutually-exclusive events, also known as disjoint events.

Mutually exclusive events are things that can’t happen at the same time. For example, you can’t run backwards and forwards at the same time. The events “running forward” and “running backwards” are mutually exclusive. Tossing a coin can also give you this type of event.

A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B) = 0. For example, suppose the sample space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.