##### Chapter 10

## Statistics

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

#### Introduction

**Statistics**and

**probability**are two tools of mathematics discipline concerning the collection, organization, processing, and analysis of quantifiable data.

**Statistics**is limited to the aspects of gathering, managing, and interpreting quantifiable data, whereas

**probability**presents predictions about the occurrence or non-occurrence of events in a varied environment.

**Statistics**and

**probability**are very closely linked due to the presence of quantifiable data and interpretation phenomenon. Additionally, these two mathematical tools also help the students in generating support for an argument with persuasive data.

There are two formulas for the addition rule of **probability**, pertaining to a **probability** related to two mutually exclusive events and **probability** related to two non-mutually exclusive events. The first formula is merely the sum of the probabilities of occurrences or non-occurrence in two events, whereas the second formula adds the aspect of deducting the **probability** of occurrence of both events simultaneously along with adding the probabilities of occurrences or non-occurrences of two events. This concept can also be understood by videos and materials available on MSVgo.

**Binomial probability **can be defined as the formulae of sourcing the exact number of successes of getting desired results in a specific number of trials. The formulae for calculating the **probability** of failure using binomial **probability** is P(F)= 1 – p (where p is the **probability** of success, and 1 is the total **probability** of event occurrence). For more information about **binomial probability, **check informative content on MSVgo.

**Bayes’ theorem** is used for finding the **probability** of occurrence or non-occurrence of an event if other probabilities are certain. The formula for this theorem is P(A|B) = P(A) P(B|A)/P(B) where P(A|B) details the time event A happens with event B, P(B|A) details the times the event B happens with event A, P(A) is the likeliness of event A happening and P(B) is the likeliness of event B happening. For more understanding, browse videos on MSVgo.

A** compound event** is a combination of two or more simple events with multiple outcomes. On the other hand, the compound probabilities are the probabilities of events pertaining to multiple outcomes and desires results within specific trails. The key example of **compound probability** can be rolling an even number on a dice as it has six possible outcomes out of which three are even; thus, the **probability** of acquiring 2,4 or 6 on dice can be defined as a **compound probability**. In other words, the **compound probability** is the mathematical likeliness of two independent events occurring in a specific environment. Generally, the **compound probability** is derived by multiplying the **probability** of first event occurrence with the **probability** of second event occurrence. However, it is to be noted that the formula for calculating the **compound probability** tends to differ on the basis of the sort of compound event being mutually exclusive and mutually inclusive. For further clarification on this concept, check videos on MSVgo.

In **probability** theory, the complement of occurrence of any event is the **probability** of that event not occurring. For instance, the complement of event A is the event NOT A. Denotation of the complimentary event is *A’* or *A**c**. *If event A is it will rain today, the complement event *A’ *will be; it will not rain today. The commonality among complementary events is that they are mutually exclusive and exhaustive. However, if the events are mutually exclusive, they cannot occur simultaneously; however, as they are exhaustive, the sum of their probabilities needs to be 100%. For more understanding about the concept of **complementary events**, browse videos on MSVgo.

Conditional **probability** concerns the **probability** of occurrence of an event along with a relationship to one or multiple other events. For instance, if event A is of raining outside with a **probability** of 0.3 and event B is going outside with a **probability** of 0.5. The conditional **probability** will be applied when going outside is subjected to raining outside. The formula of conditional **probability** is *P(B|A) = P (A and B) / P(A)* or *P(B|A) = P(A∩B) / P(A). *Conditional **probability** is generally used in the diversified fields of calculus, politics, and insurance. This concept can also be understood by videos and materials available on MSVgo.

When a coin is flipped, there are two possible outcomes, which are either head or tail, with a 50 percent **probability** for each. The **probability** for the occurrence of the head on top or tail on top when a coin is flipped is always 50-50 due to the presence of only two alternatives. For more information and questions related to coin toss **probability**, browse the videos on MSVgo.

**Statistics** and **probability** are the two branches of mathematics that are concerned with practices that govern occurrences and non-occurrences of random events by means of collecting, analyzing, interpreting, and presenting numerical data in an efficient way. **Probability** provides the logic of uncertainty for predicting events so that actions can be taken accordingly in real-time.

*What is **probability** and **statistics** in math?*

**Probability** and **statistics** are the branches of mathematics concerned with laws and practices of governing random events by collecting, analyzing, interpreting, and displaying numerical data.

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

**Probability** concerns with conducting an analysis of chances, games, genetics, and predictions pertaining to everyday activities and presenting interpretation in numerical data on the basis of the same.

*What is the purpose of **probability**?*

**Probability** concerns with detailing the likelihood of the occurrence of some event or something in varied aspects such as a game of chances or weather pattern predictions. The likeliness of an event occurring or not occurring tend to help individuals in varied ways.

*What are the four types of **probability**?*

Classical, empirical, subjective, and axiomatic are the four types of **probability**.

*What is **statistics** in math?*

**Statistics** is the branch of mathematics that concerns the collection, analysis, and interpretation of numerical and quantitative data. **Statistics** presents numeric data using graphs for the easy and efficient understanding of the processing data pertaining to the specific topic, environment, condition, or situation.