Types Of Probability

The process of generating the probability of an event determines its probability distribution. The probability of an event is the number of favourable outcomes divided by the total number of outcomes possible.

Probability =  Number of favourable outcomes/total number of outcomes                      

There are many types of events in probability. Each event type is different and has its unique properties. This categorisation of each event helps get the mathematical calculations done easily. The probability of occurrence of an event will always lie between zero and one. There can only be one sample space for a random experiment. However, there can be many different types of events.

Probability Distribution 

A Probability distribution gives an account of the number of times different possible outcomes can occur from an experiment performed. In order to define probability distributions for the specific case of random variables, it is common to distinguish between discrete and continuous random variables. Probability distributions can be shown in tables and graphs, or formulas can also describe them.

Cumulative Probability Distribution 

• The cumulative distribution assesses the probability distribution of random variables. It can describe the probability for a discrete, continuous, or mixed variable. It is procured by adding the probability density function and getting the cumulative probability for a random variable.

• The Probability Density Function selects a random variable for any value and gives a result of its probability distribution. Solving the density function for a point can obtain its probability distribution.

• The cumulative distribution of a random variable to be calculated at a point x can be shown as Fx(X). Its resulting probability will determine that the random variable X will take a value less than or equal to x.

• These distributions represent the random variables that can have discrete values as outcomes. For example, the set of potential values for the random variable X, which indicates the number of heads that can occur when a coin is tossed twice, is 0 1, 2, and not any value between 0 and 2, such as 0.1 or 1.6.

• Examples: Bernoulli, Binomial, Negative Binomial, Hypergeometric, etc.,

Types of Probability Sampling 

Simple Random Sampling

• As the name suggests, simple random sampling is considered the simplest way of probability sampling. 

• Each person in the population has an even chance in this sample form and is included on the researcher’s master list. The sampling is done randomly by appointing subjects for the sampling from that master list. 

• For the sampling to be more appropriate, simple random sampling requires a population of more than a hundred to be more precise.

• Simple random sampling is easily understandable and creates samples that are highly representative of the population; however, conducting it is time-consuming as working with a large sample size isn’t easy.

In the process of simple random sampling, two approaches are used to reduce any biases:

• Lottery procedure: One of the oldest methods is the lottery method, a mechanical version of random sampling. In this strategy, the researcher assigns a number to each member of the population. To choose samples, researchers pluck numbers at random from a box. 

• Random numbers: A different option, including numbering the population, is to employ random numbers. A numbered table can aid this sampling process.

Stratified Random Sampling

In this type of probability sampling, the subjects are grouped into different non-overlapping categories, organised into homogeneous groups (strata)   by the research group. The final members are chosen from the various strata for research that helps in reducing the cost of conducting sampling and improving its efficiency.

Age, gender, sex, socioeconomic status, educational achievements, nationality, religion, and other classifications fall under stratified random sampling.

Proportionate Stratified Random Sampling Formula: nh =  NhNn

nh = sample size 

Nh = population size

N= size of entire population

n= size of entire sample

Systematic Sampling 

Systematic sampling is a method that involves the drafting of elements from a selected sampling frame. 

Researchers calculate the sampling interval by dividing the population size by the desired sample size. Systematic sampling is a comprehensive implementation of probability sampling in which each member of the group is selected at regular periods to form a sample.

Conclusion 

Quantum phenomena necessitate the use of probability theory. The random nature of all physical events that occur at subatomic scales and are regulated by quantum mechanics was a breakthrough discovery in early twentieth-century physics. According to the Copenhagen interpretation, the objective wave function evolves deterministically. Still, it deals with observation probabilities, with the outcome described by a wave function collapse when an observation is made. However, the abandonment of determinism favouring instrumentalism was not universally embraced. Quantum decoherence is used in some recent statistical mechanics of measurement interpretations to explain the appearance of subjectively probabilistic experimental outcomes.