When the possible outcomes of an experiment are equally likely to occur this is called as probability?

Probability is a concept that is widely used in everyday life. To a certain extent the term can be synonymous to likelihood of an event to happen. In other words, Probability can be defined as the chance of an event occurring.  Many people are familiar with probability from observing or playing games of chance, such as card games, slot machines, or lotteries. In addition to being used in games of chance, probability theory is used in the fields of insurance, investments, and weather forecasting and in various other areas. For example, a stock broker can use probability to determine the rate of return on a client's investments. Finally,  probability is the basis of inferential statistics. For example, predictions are based on probability, and hypotheses are tested by using probability. 

The oldest and most commonly used definition of probability is : 
—If an event can occur in A ways and can fail to occur in B ways, and if all possible ways are equally likely , then the probability of its occurrence is A/ ( A+B), and the probability of its failing to occur is B/ ( A+B). 

we should be familiar with basic terminology and rules in probability in order to better understand the application of probability . They are as follows: 

Probability is measured on the scale of 0 to 1. Zero probability indicates  that there is no chance that an event will happen while a probability of one indicates that an event is certain to occur.When we toss a coin, there is a chance that two things happen, tail or head, both have equal chance to happen. A chance to obtain a head is 50% and a chance to obtain a tail is also 50%. Suppose a coin is tossed once and the up face is recorded. The result we see and record is called an observation or outcome and the process of making an observation is called an experiment. The set of all possible outcomes of a probability experiment is called a sample space, which is usually denoted by S.The basic possible outcomes to an experiment are called sample points . In other words, sample points are elements of sample space.

​The total probability of all sample points within a sample space is equal 1. 

Some sample spaces for various probability experiments are shown here. 

Just as graphs are useful in describing sets of data, a pictorial method for presenting the sample space will often be useful. 
we can use Venn diagrams or tree diagrams to present sample space. 

A tree diagram is a device consisting of line segments emanating from a starting point and also from the outcome point. It is used to determine all possible outcomes of a probability experiment. 

—A retail computer store sells two basic types of personal computers (PCs): standard desktop units and laptop units. Thus the owner must decide how many of each type of PC to stock. An important factor affecting the solution is the proportion of customers who purchase each type of PC. Show how this problem might be formulated in the framework of an experiment with sample points and a sample space. Indicate how probabilities might be assigned to the sample points. (The store's records indicates that 80% of its customers purchase desktop units).

Solution

An event is the subset of sample space. 
​An event can be one outcome or more than one outcome. For example, if a die is rolled and a 6 shows, this result is called an outcome, since it is a result of a single trial. An event with one outcome is called a simple event. The event of getting an odd number when a die is rolled is called a compound event, since it consists of three outcomes or three simple events. In general, a compound event consists of two or more outcomes or simple events.
There are three basic interpretations of probability:

• Classical probability
• Empirical or relative frequency probability
• Subjective probability 

Relative Frequency probability  is the ratio of the occurrence of a singular event and the total number of outcomes. This is a tool that is often used after you collect data. You can compare a single part of the data to the total amount of data collected.

Subjective probability is a type of probability derived from an individual's personal judgment about whether a specific outcome is likely to occur. It is not based on  mathematical calculations . It reflects the subject's opinions and past experience. Subjective probabilities differ from person to person, and contains a high degree of personal bias.

The Probability of an Event  ​

           Solution

Example
—Hospital records show that 12% of all patients are admitted for surgical treatment, 16% are admitted for obstetrics, and 2% receive both obstetrics and surgical treatment. If a new patient is admitted to the hospital, what is the probability that the patient will be admitted either for surgery, obstetrics, or both? Use the additive rule of probability to arrive at the answer.

—Solution
A: {A patient admitted to the hospital receives surgical treatment]—B: {A patient admitted to the hospital receives obstetrics treatment)—P(A)=.12—P(B)=.16—P(A ∩ B)=.02—P(AUB)= P(A) + P(B)- P(A ∩ B)—              =.12+.16-.02=.26

—26% of all patients admitted to the hospital receive either surgical treatment, obstetrics treatment, or both.

All probabilities that we dicussed were unconditional probabilities because no special conditions are assumed. Sometimes, we have additional knowledge of an experiment that might affect the outcome of an experiemtn. A probability that reflects such additional knowledge is called the conditional probability of the event.