When quadratic equations come in action, you’ll be challenged with either entity or non-entity; the one whose name is written in the form – √-1, and it’s pronounced as the “square root of -1.” So, we’ll be discussing in the context of the different algebraic complex numbers’ properties. 1. When a + ib = 0 … Read more

Need for complex numbers, especially √1, to be motivated by inability to solve some of the quadratic equations Complex Numbers The complex number is defined as the combination of the imaginary number and a real number. Let’s say, a + bi So here, a = real part, whereas b = imaginary part, and lastly, i … Read more

Probability: probability of ‘not’, ‘and’ and ‘or’ events General addition rule applies to any additional events. You can use it for both disjoint events and non-disjoint events where two events are mutually exclusive. This means that if 1 event is true, the other must be false. Therefore, P(A and B), i.e. the probability of both … Read more

Probability: event An event is an outcome for any experiment and it is denoted by a capital letter. It is the basic element to which probability is applied. When an experiment is performed, an event either happens, or it doesn’t. A simple event is denoted by a E with a subscript where the event is … Read more

Probability: Connections with the theories of earlier classes Nothing in life is certain and in all our activities, we gauge the chances of successful outcomes, from business to medicine to the weather. A probability helps in understanding a quantitative description of likelihoods associated with various outcomes. It helps in developing a bridge between descriptive and … Read more

Probability: Axiomatic (set theoretic) probability Given an experiment and a sample space, probability is used to designate each event A a number P(A), called the probability of the event A. This designation provides a precise measure of the chance that A will occur. To ensure that the probability assignments are consistent with the intuitive notions … Read more

Probability: mutually exclusive events Mutually exclusive events are called nonempty events which can be defined on the same sample space with each event while excluding the occurrence of the other.In other words, these events share no common elements. Mutually Exclusive Events There are several ways to express the concept of mutually exclusive, For instance, f … Read more

Probability: random experiments – exhaustive events When a sample space is divided into multiple mutually exclusive events where their union forms the sample space itself, then these events are called exhaustive events.A collectively exhaustive event contains all the possible elementary events for a certain experiment under consideration: In probability theory and logic, a set of … Read more

Probability: Occurrence of events: not, and, or events The event, E, is any subset of the sample space, S that is a set of outcomes which does not necessarily need to have all outcomes for random phenomena. The event, E, is said to have occurred if after the outcome is observed then the outcome lies … Read more

Probability: random experiments – sample spaces The sample space, S, for a random phenomenon is defined as the set of all possible outcomes. It is basically a list of unique, non-overlapping possible outcomes of random circumstances shown in a set representation denoted by symbol ‘S’. The outcomes must be mutually exclusive and exhaustive from each … Read more