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Probability And Statistics: Definition, Theory, Formula & Solved Examples!!

Probability And Statistics: Definition, Theory, Formula & Solved Examples!!

Probability and Statistics are the two most essential chapters in mathematics. This mini-lesson will be very useful if you are in classes 10, 11, or 12. 

Probability is “chance” or an event that is likely to happen. Statistics is completely about the collection of data and handling it in a way using different techniques. Statistics help us to represent complex data in a very simple manner. 

Often students avoid the importance of these chapters and focus on other units. Both chapters have significant weightage in the board and competitive examination. Students can easily grab the fundamentals of probability and statistics using NCERT Solution for class 10 maths.  

This blog will touch every nerve of Probability and Statistics, including definitions, terms, formulas, and solved examples. Let us dive into the topic. 

Probability

Table of Content
What is ProbabilityProbability FormulaTerms Used in ProbabilityTopics in ProbabilityImportance of ProbabilitySolved Examples of Probability

What is Probability

Probability deals with “random event” or “chance.” The branch of physics which deals with the possibility of outcomes in random events are probability. The value from 0 to 1 denotes probability. It also explains how likely something is to happen.

For example, what is the probability of getting a head when we toss a coin?

A coin has two sides one is the head, and the other is the tail. If we flip the coin, it is a high probability of coming either hear or tail result, so the probability of getting a head will be 1/2.  

What is the probability of getting the Number two on the dice?

Dice consist of numbers 1 to 6. The possibility of getting Number two out of six is 1/6.

Probability Formula

Probability is the ratio of the Number of favorable outcomes to total outcomes.

Probability = Number of favorable outcomes/ total Number of outcomes

P(E) = n(A)n(S)

Where

P(E) = Probability

n(A) = Number of favorable outcomes

n(S) = total number of outcomes

Terms Used in Probability

Random Experiment

All those experiments whose outcomes can not be predicted until it noticed are called random experiments. E.g., if you throw a dice randomly, the possibility of getting the number 3 on the dice is uncertain. You can get any random number from 1 to 6. 

Sample Space

Sample Space is the set of the possibility of all the results or outcomes in a random experiment. E.g., if we throw dice, the set of all the possible outcomes is 1-6.  

Event

It is the outcome or result of an experiment; for, e.g., if you flip a coin, getting a tail is an event.

Random Event

The unpredicted events or the possibility of outcomes significantly less are known as Random Events. The formation of the rainbow is an example of a random event.

Trial

The Number of experiments in the experiment process is called a trial. For example, flipping the coin is a trial.

Check out- NCERT Solutions For Class 12 Maths

Topics in Probability

To pass the examination with flying colors, students are required to cover the topics given in their syllabus. Here we have listed all the basic probability topics which are very crucial for the board as well as competitive examinations.   

Addition Rule of ProbabilityBinomial ProbabilityBayes Theorem
Compound EventsCompound ProbabilityComplementary Events
Conditional ProbabilityComplementary EventsCoin Toss Probability
Dependent EventsExperimental ProbabilityGeometric Probability
Independent EventsMultiplication Rule of ProbabilityMutually Exclusive Events
Properties of ProbabilityProbability LineProbability without Replacement
Random VariablesSimple EventSample Space
Tree DiagramTheoretical ProbabilityTypes of Events
Experimental ProbabilityAxiomatic Probability

Importance of Probability

  • It helps us to solve real-life problems.
  • It is widely used in medical science, weather forecasting, biological science, data science, etc.  
  • It increases the problem-solving ability of students. 

Solved Examples of Probability

Question-1: Find the probability of getting two on rolling dice?

All sample space= {1, 2, 3, 4, 5, 6}

Total number of outcomes = n(S) = 6

Let A represent the event of getting 2

Number of favourable outcomes = n(A) = 1

i.e. A = {2}

P(A) = n(A)/n(S) = 1/6

Hence getting 2 on rolling dice is = ⅙

The probability of getting two on rolling dice is ⅙. 

Question-2: What is the probability of getting any face card from a pack of cards?

A deck of cards has 52 cards.

Number of total outcomes n(S) = 52

Suppose E be the event of getting face cards

Number of favorable events((considered Jack, Queen, and King only)

) = n(E) = 4 x 3 = 12 

Accoding to probability formula = number of favorable outcomes/total number of outcomes

= 12/52

= 3/13

The possibility of getting a face card in the deck of cards is 3/13.

Statistics

Table of Content
What is StatisticsStatistics FormulaTopics in StatisticsImportance of StatisticsSolved Examples on Statistics

What is Statistics

Statistics is the branch of applied mathematics that deals with the collection, analysis, interpretation, and organization of data handling using different techniques. 

From collecting data on the country’s population and economy to an In-depth study of data analysis, every domain uses statistics for qualitative and quantitative approaches. 

Statistics Formula

Topics in Statistics

Box and Whisker PlotsComparing Two MeansComparing Two Proportions
Categorical DataCentral TendencyCorrelation
Data HandlingDegree of freedomEmpirical Rule
Frequency Distribution TableFive Number SummaryGraphical Representation of Data
HistogramMeanMedian
ModeData RangeRelative Frequency
Population and SampleScatter PlotsStandard Deviation
Ungrouped DataVarianceData Sets

 Importance of Statistics

  • It helps us analyze and handle the data.
  • It represents complex data in a very easy-to-understand format.
  • It provides a better understanding of data using a graphical representation. 

Check Out More– Maths Symbols

Solved Examples on Statistics

Question-1:Find the mean of the first ten natural numbers.

 The first ten natural numbers are 1,2,3,4,5,6,7,8,9 and 10

 Mean = sum of given all the numbers/total number 

(1+2+3+4+5+6+7+8+9+10)/10

= 5.5

Question-2: Find the mode of following observations

            4,5,6,5,8,3,4,8,2,7,8

We can see that eight occurs maximum times, so the mode of the following observations is 8. 

Frequently Asked Questions(FAQs)

1. What is the probability formula?

Probability is defined as the ratio of the Number of outcomes to the total Number of outcomes. 

Probability = Number of favorable outcomes /total Number of outcomes

2. What is the byes theorem and its formula?

The byes theorem is used to determine conditional probability. According to byes theorem

P(A|B) = P(B|A)P(A)P(B)

3. How many types of probability are there in mathematics?

There are majorly three types of probability 

1. Theoretical probability

2. Experimental probability

3. Axiomatic probability

4. What are the types of statistics?

There are two types of statistics.

1. Descriptive statistics

2. inferential statistics

5. How to calculate the median?

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