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Conditional Probability, Solved Examples | Class 12 Math Notes Study Material Download Free PDF

January 17, 2025 by Neeraj Anand, Param Anand
Imagine a student who takes leave from school twice a week excluding sunday. If it is known that he will be absent from school on tuesday then what are the chances that he will also take a leave on saturday in the same week? It is observed that in problems where the occurrence of one event affects the happening of the following event. These cases of probability are known as conditional probability. Let us learn its definition mathematically.

Imagine a student who takes leave from school twice a week excluding Sunday. If it is known that he will …

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Multiplication Rule of Probability | Proof & Solved Examples | Class 12 Math Notes Study Material Download Free PDF

January 17, 2025 by Neeraj Anand, Param Anand
The multiplication rule of probability explains the condition between two events. For two events a and b associated with a sample space s set a∩b denotes the events in which both events a and event b have occurred. Hence, (a∩b) denotes the simultaneous occurrence of events a and b. Event a∩b can be written as ab. The probability of event ab is obtained by using the properties of conditional probability.

The multiplication rule of probability explains the condition between two events. For two events A and B associated with a …

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Independent & Mutually Exclusive Events in Probability-Definition, Venn Diagram & Solved Examples | Class 12 Math Notes Study Material Download Free PDF

January 17, 2025 by Neeraj Anand, Param Anand
Independent events are those events whose occurrence is not dependent on any other event. For example, if we flip a coin in the air and get the outcome as head, then again if we flip the coin but this time we get the outcome as tail. In both cases, the occurrence of both events is independent of each other. It is one of the types of events in probability. Let us learn here the complete definition of independent events along with its venn diagram, examples and how it is different from mutually exclusive events.

Independent events are those events whose occurrence is not dependent on any other event. For example, if we flip a …

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Oxoacids of Halogens-Properties, Structure,Hypochlorous Acid, Chlorous Acid, Perchloric Acid, Interhalogen Compounds, FAQs

October 2, 2025December 26, 2024 by Neeraj Anand, Param Anand
The elements of group 17 from top to bottom are fluorine, chlorine, bromine, iodine, and astatine. They are referred to as halogens because they create salt. This group’s members are very similar to one another. They have a consistent pattern of physical and chemical features. The valence shell of each of these elements contains seven electrons. Their electronic setup is ns2 np5.

The elements of Group 17 from top to bottom are fluorine, chlorine, bromine, iodine, and astatine. They are referred to …

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Allotropes of Phosphorus, White Phosphorus, Red Phosphorus , Black Phosphorus, Phosphorus Trichloride (PCl3), Phosphorus Pentachloride (PCl5)

October 2, 2025December 26, 2024 by Neeraj Anand, Param Anand
Phosphorus is an element that cannot be found naturally in our environment. It is highly reactive. Phosphorus is a chemical element with an atomic number of 15, which means it has 15 protons and 15 electrons in its atomic structure. Phosphorus has the chemical symbol p.

Phosphorus is an element that cannot be found naturally in our environment. It is highly reactive. Phosphorus is a chemical …

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Oxides of Nitrogen-Preparation, Properties, Structure, Uses of Nitrogen Dioxide (NO2), Nitric Acid (HNO3), Nitrous Oxide (N2O), Nitric oxide (NO), FAQs

September 28, 2025December 26, 2024 by Neeraj Anand, Param Anand
Nitrogen combines with oxygen to generate nitrogen oxides in a variety of forms. Its oxides have distinct oxidation states, ranging from +1 to +5. Nitrogen oxides with a greater oxidation state are more acidic than those with a lower oxidation state.  

Nitrogen combines with oxygen to generate nitrogen oxides in a variety of forms. Its oxides have distinct oxidation states, ranging …

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Ammonia(NH3)-Structure, Physical & Chemical Properties, Preparation, Uses, FAQs

October 3, 2025December 26, 2024 by Neeraj Anand, Param Anand
Ammonia (nh₃) is a colorless gas with a sharp, pungent odor. It is a compound of nitrogen and hydrogen and plays a crucial role in both the industrial sector and biological processes.

Ammonia (NH₃) is a colorless gas with a sharp, pungent odor. It is a compound of nitrogen and hydrogen and …

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Dinitrogen(N2)-Preparation, Reactions, Properties, Uses, Nitrogen Cycle, Occurence, FAQs

October 2, 2025December 26, 2024 by Neeraj Anand, Param Anand
Nitrogen is the lightest element in periodic table group 15, also known as the pnictogens. Dinitrogen, a colourless and odourless diatomic gas with the formula n2, is formed when two atoms of the element join together at stp.  

Nitrogen is the lightest element in Periodic Table Group 15, also known as the pnictogens. Dinitrogen, a colourless and odourless …

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Nitrogen Family-Group 15 Elements, Periodic Trends, Physical & Chemical Properties, Anomalous Properties of Nitrogen

September 29, 2025December 26, 2024 by Neeraj Anand, Param Anand
The contemporary periodic table, devised by dimitri mendeleev, lists all known elements according to their atomic number, which is unique to each element. The periodic table was created as a result of such an arrangement. The items with comparable qualities were grouped together in a column.

The contemporary periodic table, devised by Dimitri Mendeleev, lists all known elements according to their atomic number, which is unique …

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Temperature Dependence of the Rate of a Reaction-Arrhenius Equation, Threshold energy, Activation energy

December 25, 2024 by Neeraj Anand, Param Anand
The meal cooks slowly if the gas is kept at a low temperature while cooking. When we raise the temperature to its highest setting, however, the food cooks quickly. As a result, increasing the temperature increases the rate of a reaction. The arrhenius equation helps explain this rate-temperature relationship. Let’s have a look at this equation and see how it works.

The meal cooks slowly if the gas is kept at a low temperature while cooking. When we raise the temperature …

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Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Miscellaneous Exercise Class 12 Chapter-13 Math Notes PDF Free Download (Set-2)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

NCERT Solutions Probability Miscellaneous Exercise Class 12 Chapter-13 Math Notes PDF Free Download (Set-1)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

NCERT Solutions Probability Exercise 13.3 Class 12 Chapter-13 Math Notes PDF Free Download (Set-2)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Exercise 13.3 Class 12 Chapter-13 Math Notes PDF Free Download (Set-1)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Exercise 13.2 Class 12 Chapter-13 Math Notes PDF Free Download (Set-2)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Exercise 13.2 Class 12 Chapter-13 Math Notes PDF Free Download (Set-1)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Exercise 13.1 Class 12 Chapter-13 Math Notes PDF Free Download (Set-1)

Download free NCERT Solutions for Class 12 Math Chapter 13 Probability from Anand Classes. Get clear, step-by-step solutions and printable notes for exam preparation.

Probability NCERT Solutions Exercise 13.1 Class 12 Chapter-13 Math Notes PDF Free Download (Set-2)

Download free NCERT Solutions for Class 12 Chapter 11 Three Dimensional Geometry from Anand Classes. Clear, step-by-step maths notes in PDF format.

Three Dimensional Geometry NCERT Solutions Miscellaneous Exercise Chapter-11 Class 12 Math Notes PDF Free Download

Download free NCERT Solutions for Class 12 Chapter 11 Three Dimensional Geometry from Anand Classes. Clear, step-by-step maths notes in PDF format.

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