Chapter 5 – Statistics and Probability

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

Introduction

Statistics and Probability are somewhat related to each other but probability is concerned with chance and statistics is related to how we handle data using various techniques. If you are preparing for any competitive exams, then this article will prove to be very insightful. In this article, we have discussed the fundamentals of Statistics and Probability in brief. We hope this article helps you grasp the concept conveniently.

The addition rule of probability is the fourth rule. When at the same time, two events cannot occur then they are called disjoint or mutually exclusive. Let’s give you an example to enhance your understanding:

Consider the following two events:

C – a person has blood type AB+

D – a person has blood type A.

Now, if you consider both the events and if we assume that every person has only one blood type. Therefore it is impossible that events C and D will occur together. Here the event is said to be disjoint.

Binomial Probability

It is defined, as when two possible outcomes of an experiment are probable. It is called the binomial experiment. It is used to calculate the probability of success for binomial distributions. The formula is:-

(x: n,p) = nCxpxq(n-x)

n – Number of trials
p – Probability of success
q – Probability of failure
x – Number of success
b – Binomial Probability

Bayes Theorem

Bayes Theorem explains the probability of occurrence of an event related to any condition. It is also called the formula for the probability of causes. By making use of the definition of conditional probability and density, the Bayes theorem can be derived for the events and random variables. It is mostly used to find the reverse probabilities if the conditional probability is known of the event. The Bayes theorem formula is

P(A|B) = P(A∩B) / P(B)

Compound Events

As compared to the simple event, when an event consists of more than one single point of the sample space, then it is known as a compound event.

For example, if S = (45,65,76,88,90), E1 = (45, 88), E2 = (65,45,90) then E1 and E2 represent two compound events.

Compound Probability

It refers to the probability of two or more independent events, both occurring at the same time. When an outcome of one event does not affect the outcome of another event, then that event is called an independent event. The formula is P(A and B) = P(A) × P(B)

Complementary Events

There exists another event E1′ for every event E1 that shows the remaining elements of the sample space S.

E1 = S − E1‘

Conditional Probability

Concerning A when event B has already occurred that occurrence is probable of an event A, then it is known as Conditional Probability. The formula is

P (A|B) = N(A∩B) / N(B).

P (A|B) – It shows the probability of occurrence of A and B has already taken place,

N (A∩B) – Number of elements common to both A and B.

N (B) – it represents the number of elements in B which cannot be equal to zero.

Coin Toss Probability

Probability is all about chance. If the probability of any event is high, then it is likely to occur, and whose probability is low, then that event is unlikely to occur. Like if asked what will be the probability of getting a tail if a coin is tossed, you will say that there is a 50% probability of getting a tail. It is simply because you are aware of the fact that either it is head or tail.

Formula

• Probability of getting a tail = No. of outcomes to get tail/No. of possible outcomes
• Probability of a certain event = No. of favourable outcomes/Total number of possible outcomes

What is the probability and statistics in math?

Answer. It is among the branches of mathematics that deals with analysis, interpretation, and with the laws controlling various events.

What is the role of probability in statistics?

Answer.  It is used to predict the results of many experiments having some assumptions. It is used to calculate the probability between prediction and results.

What is the purpose of probability?

Answer. It helps measure how likely something is to happen. It is mostly used to analyse the event and set possible results. Meteorologists too use probability to predict the weather as well.

What are the four types of probability?

Answer. The following are the four types of probability:

• Classical
• Empirical
• Subjective
• Axiomatic

What is the statistics in math?

Answer. It is a method in which probability theory is used. In other words, it is a collection, interpreting, and summarising of data. It is widely used by Mathematicians and statisticians.

Statistics and Probability are the two most important topics in Mathematics. Professionals widely use it, and business people to ascertain profit and loss; therefore, it becomes more important to understand this concept accurately.

We help you to comprehend Statistics and Probability first, with in-depth concept notes and explanatory video on the MSVGo app. MSVGo app has a video library that explains concepts with examples or explanatory visualisations or animation. To learn more about it, check out the MSVgo app. Stay tuned with the MSVGo app and happy learning!

High School Physics

• Alternating Current
• Atoms
• Communication Systems
• Current Electricity
• Dual nature of Radiation and Matter
• Electric Charges and Fields
• Electricity
• Electromagnetic Induction
• Electromagnetic Waves
• Electrons and Photons
• Electrostatic Potential and Capacitance
• Fluid Pressure
• Force and Acceleration
• Force And Laws Of Motion
• Gravitation
• Internal Energy
• Kinetic Theory
• Law of motion
• Light – Reflection And Refraction
• Magnetic Effects Of Electric Current
• Magnetism and Matter
• Management Of Natural Resources
• Mechanical properties of Fluids
• Mechanical properties of Solids
• Motion
• Motion in a plane
• Motion in a straight line
• Moving Charges and Magnetism
• Nuclear Energy
• Nuclei
• Oscillations
• Our Environment
• Paths of Heat
• Physical world
• Ray optics and optical instruments
• Semiconductor Devices
• Semiconductor Electronics: Materials, Devices and Simple Circuits
• Simple Machines
• Sound
• Sources Of Energy
• Specific and Latent Heats
• Spherical Mirrors
• Static Electricity
• Systems of Particles and Rotational motion
• Thermal properties of matter
• Thermodynamics
• Units and Measurement
• Vectors, Scalar Quantities and Elementary Calculus
• Wave Optics
• Waves
• Work, Power and Energy

High School Chemistry

• Acids, Bases and Salts
• Alcohols, Phenols and Ethers
• Aldehydes, Ketones and Carboxylic Acids
• Aliphatic and Aromatic Hydrocarbons
• Alkyl and Aryl Halides
• Amines
• Analytical Chemistry
• Atomic Structure
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• Basic concepts of Chemistry
• Biomolecules
• Carbon And Its Compounds
• Carboxylic acids and Acid Derivatives
• Chemical Bonding and Molecular Structures
• Chemical Energetics
• Chemical Equilibria
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• Chemical Reactions And Equations
• Chemical Reactions and Their Mechanisms
• Chemistry in Everyday Life
• Chemistry of p-Block elements
• Chemistry of Transition and Inner Transition
• Classification of Elements
• Coordination Compounds
• Cyanide, Isocyanide, Nitro compounds and Amines
• Electrochemistry
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• Elements, Compounds and Mixtures
• Environmental Chemistry
• Equilibrium
• Ethers and Carbonyl compounds
• Haloalkanes and Haloarenes
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• Introduction to Organic Chemistry
• Ionic equilibria
• Matter
• Matter Around Us
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• Mole Concept and Stoichiometry
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• Periodic Classification of Elements
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• Preparation, Properties and Uses of Compounds
• Principles and Processes of Isolation of Elements
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• Relative Molecular Mass and Mole
• States of Matter
• Structure Of The Atom
• Study of Compounds
• Study of Gas Laws
• Study of Representative Elements
• Surface Chemistry
• The d-block and f-block elements
• The Gaseous State
• The p-Block Elements
• The Periodic Table
• The s-Block Elements
• The Solid State
• Thermodynamics

High School Biology

• Absorption and Movement of Water in Plants
• Anatomy of Flowering Plants
• Animal Kingdom
• Bacteria and Fungi-Friends and Foe
• Biodiversity and Conservation
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• Breathing and Exchange of Gases
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• Circulation
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• Diversity In Living Organisms
• Ecosystem
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• Genes and Chromosomes
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• How Do Organisms Reproduce?
• Human Diseases
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• Integumentary System- Skin
• Kingdom Fungi
• Kingdom Monera
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• Life Processes
• Locomotion and Movement
• Microbes in Human Welfare
• Mineral Nutrition
• Molecular Basis of Inheritance
• Morphology of Flowering Plants
• Neural Control And Coordination
• Nutrition in Human Beings
• Organism and Population
• Photosynthesis
• Photosynthesis in Higher Plants
• Plant Growth and Development
• Plant Kingdom
• Pollination and Fertilization
• Pollution; Sources and its effects
• Principles of Inheritance and Variation
• Reproduction and Development in Angiosperms
• Reproduction in Organisms
• Reproductive Health
• Respiration in Human Beings
• Respiration in Plants
• Respiratory System
• Sexual Reproduction in Flowering Plants
• Strategies for Enhancement in Food Production
• Structural Organisation in Animals
• Structural Organisation of the Cell
• The Endocrine System
• The Fundamental Unit Of Life
• The Living World
• The Nervous System and Sense Organs
• Tissues
• Transpiration
• Transport in Plants

High School Math

• Algebra – Arithmatic Progressions
• Algebra – Complex Numbers and Quadratic Equations
• Algebra – Linear Inequalities
• Algebra – Pair of Linear Equations in Two Variables
• Algebra – Polynomials
• Algebra – Principle of Mathematical Induction
• Binomial Theorem
• Calculus – Applications of Derivatives
• Calculus – Applications of the Integrals
• Calculus – Continuity and Differentiability
• Calculus – Differential Equations
• Calculus – Integrals
• Geometry – Area
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• Geometry – Conic Sections
• Geometry – Constructions
• Geometry – Introduction to Euclid’s Geometry
• Geometry – Three-dimensional Geometry
• Geometry – Lines and Angles
• Geometry – Straight Lines
• Geometry – Triangles
• Linear Programming
• Matrices and Determinants
• Mensuration – Areas
• Mensuration – Surface Areas and Volumes
• Number Systems
• Number Systems – Real Numbers
• Permutations and Combinations
• Probability
• Sequence and Series
• Sets and Functions
• Statistics
• Trignometry – Height and Distance
• Trignometry – Identities
• Trignometry – Introduction

Middle School Science

• Acids, Bases And Salts
• Air and Its Constituents
• Basic Biology
• Body Movements
• Carbon and Its Compounds
• Cell – Structure And Functions
• Changes Around Us
• Chemical Effects Of Electric Current
• Coal And Petroleum
• Combustion And Flame
• Components Of Food
• Conservation Of Plants And Animals
• Crop Production And Management
• Electric Current And Its Effects
• Electricity And Circuits
• Elements and Compounds
• Fibre To Fabric
• Food production and management
• Force And Pressure
• Forests: Our Lifeline
• Friction
• Fun With Magnets
• Garbage In, Garbage Out
• Getting To Know Plants
• Health and Hygiene
• Heat
• Hydrogen
• Life Processes: Nutrition in Animals and Plants
• Materials: Metals And Non-Metals
• Matter and Its States
• Metals and Non-metals
• Micro Organisms: Friend And Foe
• Motion And Measurement Of Distances
• Motion And Time
• Nutrition In Animals
• Nutrition In Plants
• Organization in Living Things
• Our Environment
• Physical And Chemical Changes
• Pollution and conservation
• Pollution Of Air And Water
• Reaching The Age Of Adolescence
• Reproduction In Animals
• Reproduction In Plants
• Respiration In Organisms
• Rocks and Minerals
• Separation Of Substances
• Simple Machines
• Soil
• Some Natural Phenomena
• Sorting Materials Into Groups
• Sound
• Stars And The Solar System
• Structure of Atom
• Synthetic Fibers And Plastics
• The Living Organisms And Their Surroundings
• Transfer of Heat
• Transformation of Substances
• Transportation In Animals And Plants
• Universe
• Waste-water Story
• Water: A Precious Resource
• Weather, Climate And Adaptations Of Animals To Climate
• Winds, Storms And Cyclones

Middle School Math

• Area and Its Boundary
• Boxes and Sketches
• Data Handling
• Fun With Numbers
• Heavy and Light
• How Many
• Long And Short
• Mapping
• Measurement
• Money
• Multiplication and Factors
• Multiply and Divide
• Numbers
• Parts and Wholes
• Pattern Recognition
• Patterns
• Play With Patterns
• Rupees And Paise
• Shapes And Angles
• Shapes And Designs
• Shapes and Space
• Similarity
• Smart Charts
• Squares
• Subtraction
• Tables And Shares
• Tenths and Hundredths
• Time