January 27, 2023 Ultimate News Hub

Probability of two events

The likelihood of occurrence of an event can be termed as a probability. The value of probability is between 0 and 1. 0 – the impossibility of the event and 1 – certainty. If the value of the probability is more, then the event is more likely to happen. For example, in tossing a coin, the two outcomes are a head or a tail. The probability of a head or a tail is 0.5 each as they are equally probable. 

The word probability is derived from the Latin word namely probabilitas, which can also mean “probity”. Probability is the ratio of the number of outcomes to the number of outcomes in total. It varies as different types of events are studied like conditional, independent or mutually exclusive. This article answers the question of how to find probability of two events. On this page, steps to determine the probability of normal distribution are also discussed.

A few concepts related to events are discussed below: 

The complement of event A is described as the probability of non-occurrence of event A and denoted as P (A’). 

The union of events A and B is defined as any or all of the events being considered to occur. It is denoted as P (A U B). 

The intersection of A and B is the probability that two events A and B both occur and is written as P (A ⋂ B). 

The two events are said to be independent events when the result of the event occurring first does not affect the result of the second event. 

Normal distribution

The normal distribution belongs to the group of continuous probability distributions. It is defined by the normal equation. The probability density function is written as

In the above function, x refers to the normal random variate, μ – the mean, σ – standard deviation, π ≅ 3.14, and e ≅ 2.72. x in the normal equation is termed as the normal random variable. The concept of a normal curve is associated with normal distribution. It is dependent on the mean and standard deviation. The position of the centre of the graph is determined by the mean whereas the height and width are determined by the standard deviation. A bell-shaped curve that is symmetric represents the normal distribution. A tall and narrow curve is obtained when the value of standard deviation is smaller and when the standard deviation is bigger, the curve is tiny and wide. The following points provide a solution to the question – how to find probability of normal distribution in an easy and understandable way. 

  • The area in total under the normal curve is equal to 1.
  • The probability associated with a random variable x equated to any particular value is 0.
  • P [X > a] = the area under the normal curve bounded by a and + ∞.
  • P [X < a] = the area under the normal curve bounded by a and – ∞.

Any normal curve follows a rule called an empirical rule or 68-95-99.7 rule.

  • 68% of the values lie inside 1 standard deviation of the mean.
  • 95% of the values lie inside 2 standard deviations of the mean.
  • 99.7% of the values lie inside 3 standard deviations of the mean.

Some of the major applications of normal distribution include the central limit theorem,  least-squares fitting, regression problems, position of a particle that experiences diffusion.  

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