The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

You’ll find Statistics and Probability to be two very interesting topics. Not only will you enjoy solving them in school & college, but you’ll find them applicable in real life quite often! Let’s look at them in detail with simplified explanations here.

Probability denotes the probability that some unpredictable occurrence would occur. The purpose of this word is to verify the degree to which it is possible that some occurrence may occur. What is the **coin toss probability **of having a head, for instance? The solution to this question is based on the number of results that are probable. The probability here is that the result will be either head or tail. So, the chance of a head arriving, as a result, is 1/2.

The chance is the estimate of an event’s possibility of occurring. It tests the event’s certainty. The probability formula is given by;

P(E) = Number of favourable results/Total results number

P(E) = n(E)/n n(e)/n (S)

Here,

N(E) = Event Number beneficial to Event E

n(S) = Complete number of outcomes

Statistics is a process of gathering and summarizing the results. Stats are used for data processing, whether it is the study of the country’s population or its economy.

In many disciplines, such as economics, psychology, geology, weather forecasts, etc., statistics have a wide variety. The data for research obtained here may be quantitative or qualitative. There are also two types of quantitative data: discrete and continuous. There is a constant value for discrete data, while continuous data is not fixed data, it has a variety. This definition uses multiple words and formulas. To explain them, see the following table below.

There are several terminologies used in the definitions of probability and statistics, such as:

**1. Random Experiment **

A random experiment is considered an experiment whose results can not be projected until it is noticed. For starters, the outcome is unknown to us when we throw dice randomly. We can get any output that goes from 1 to 6. This experiment is, thus, spontaneous.

**2. Space Sample **

The set of all potential outcomes or effects of a random experiment is a sample space. Suppose, if we randomly throw a dice, then the sample space for this experiment will be all possible dice throwing effects, such as:

The Space Sample = {1,2,3,4,5,6}

**3. Random Variables**

The variables that denote a random experiment’s potential effects are called random variables. They belong to two types:

- Random Discrete Variables
- Random Continuous Variables

Only those distinct values which are countable are taken by discrete random variables.

Whereas an infinite number of potential values might be taken by continuous random variables.

**4. Independent Event **

If the likelihood of one occurrence happening has no effect on the likelihood of another event, then all events are identified as independent of each other. For eg, if you flip a coin and throw dice at the same time, the possibility of having a ‘head’ is independent of the risk of getting a 6 in a dice. A **complementary event** is a chance when an event occurs if and only if the other event does not occur.

**5. Mean **

The sum of the random values of the potential consequences of a random experiment is the mean of a random variable. In simplistic words, it is the **compound probability** of the random experiment’s potential outcomes, replicated over and over again or a number of times. The expectation of a random variable is often called that.

**6. Expected Value **

The predicted value is a random variable average. For a random experiment, it is the assumed value that is considered. It is sometimes called expectation, first moment, or mathematical expectation. If we roll dice with six faces, for instance, then the predicted value will be the average value of all possible values, i.e. 3.5.

**7. Variance**

Basically, the variance shows us how the random variable’s values are distributed around the mean value. The distribution of the space of the sample over the mean is defined.

In this chapter, we learned about the basics of statistics and probability. We learned about their formulas, different terms, and their application in mathematics. We learned about the** addition rule of probability**, and statistics concepts like **compound events**.

**1. What is the role of probability in statistics? **

Probability is essentially how likely there is to be anything. Whenever we are uncertain about an event’s result, we should ask about the probability of those outcomes-how probable they are. Statistics is called the study of events controlled by chance.

**2. What are the 3 types of probability? **

Three main types of probability exist:

- Theoretical Probability.
- Experimental Probability.
- Axiomatic Probability.

**3. What does OR mean in probability?**

We sometimes want to know the possibility of having one outcome or another. If events are mutually exclusive and we want to know the chance of one occurrence or another, then we should use the law of OR. Mostly seen in **conditional probability**.

**4. What is the formula of probability?**

Probability of occurrence of incident P(E) = Number of favorable events/Total number of events.

**5. How do you calculate probability and statistics? **

Probability of occurrence of incident P(E) = Number of favorable events/Total number of events.

Formula to calculate statistics

- Population mean = μ = ( Σ Xi ) / N.
- Population standard deviation = σ = sqrt [ Σ ( Xi – μ )^2 / N ]
- Population variance = σ2 = Σ ( Xi – μ )^2 / N.

To learn more about **statistics and probability** through simple, interactive, and explanatory visualizations, download the MSVgo app.