If in a random experiment, there are n mutually exclusive and equally likely elementary events and

m of them are favourable to an event A, then the probability of p of happening of A, denoted by P(A),

is defined as the ratio (m/n).

The probability q of failure of event A is

Exhaustive events: The total number of possible outcomes of a random experiment is called exhaustive events.

(i) In tossing a coin, exhaustive events are two.

(ii) In throwing a die, the exhaustive number of cases is 6.

Mutually Exclusive: The events are said to be mutually exclusive if they can not occur simultaneously in a single draw.

When a coin is tossed, it can show either a head or a tail.

If we toss a tail, we can not get a head.

If we toss a head, we can not get a tail.

Thus these events are mutually exclusive.

The addition rule:

When two events are mutually exclusive, we can work out the probability of either of them occurring

by adding together the separate probabilities.

Multiplication Theorem of Probability:

If two events A and B are independent, then the probability that they will both occur is equal

to the product of their individual probabilities.

i.e., P(A and B) = P(A) × P(B)

In set notation:  P(A ∩ B) = P(A) × P(B)

XII M B Q S ISC Probability 2023 (1) XII M B Q S ISC Probability 2023 (2) XII M B Q S ISC Probability 2023 (3)

 

 

 

ISC              Class 12                   Mathematics Previous Years Board Questions Solutions of Previous years Board Questions Inverse Trigonometric Functions (2000 to Sem 1-2021) Inverse Trigonometric Functions (2000 to Sem 1-2021) Inverse Trigonometric Functions – (2020 to 2023)  Inverse Trigonometric Functions – (2020 to 2023)  Matrices (2000 to Sem 1 – 2021) Matrices (2000 to Sem 1-2021) Matrices –(2020 to 2023)  Matrices- (2020 to 2023) Determinants (2000 to Sem1-2021) Determinants (2000 to Sem1-2021) Determinants (2020 to 2023) Determinants (2020 to 2023) Differentiation (2000 to Sem 1- 2021) Differentiation (2000 to Sem 1- 2021) Differentiation (2020 to 2023) Differentiation (2020 to 2023) L’ Hospital’s Rule (2001 to Sem1-2021) L’ Hospital’s Rule (2001 to Sem1-2021) Rolle’s Theorem and Lagrange’s Mean Value Theorem (1998 to 2020) Rolle’s Theorem and Lagrange’s Mean Value Theorems (1998 to 2020) Maxima and Minima (2000 to Sem 1-2021) Maxima and Minima (2000 to Sem 1 – 2021) Maxima and Minima (2020 to 2023) Maxima and Minima (2020 to 2023) Integration (1990 – 2011) Integration (1990 – 2011) Integration (2012 to 2022) Integration (2012 to 2022) Integration (2020 to 2023) Integration (2020 to 2023) Differential Equations (1991 to 2005) Differential Equations (1991 to 2005) Differential Equations (2006 to 2022) Differential Equations (2006 to 2022) Differential Equations (2020 to 2023) Differential Equations (2020 to 2023) Probability (Addition and Multiplication Theorem-Conditional Probability) (1993 to 2022) Probability (Addition and Multiplication Theorem, Conditional Probability) (1993 to 2022) Probability (Baye’s Theorem) (2000 to Sem 2-2022) Probability (Baye’s Theorem) (2000 to Sem 2-2022) Probability (Probability distribution and Binomial distribution) (1992 to 2020) Probability (Probability distribution and Binomial distribution) (1992 to 2020) Probability – 2023 Application of Calculus in Commerce and Economics (2005 to Sem 1-2021) Application of Calculus in Commerce and Economics (2005 to Sem 1-2021) Application of Calculus in Commerce and Economics (2020 to 2023)  Application of Calculus in Commerce and Economics (2020 to 2023) Linear Programming (2008 to Sem 2-2022) Linear Programming (2008 to 2022) Linear Programming (LPP) (2020 to 2023) Linear Programming (LPP) (2020 to 2023) Linear Regression (2005 to 2013)  Linear Regression – (2005 to 2013)  Linear Regression (2014 to 2022) Linear Regression –  (2014 to 2022)   Linear Regression (2020 to 2023) Linear Regression (2020 to 2023)

MCQ              Class 12         Mathematics Relations and Functions Inverse Trigonometric Functions Matrices Determinants Continuity and Differentiability Tangents and Normals Maxima and Minima Increasing and Decreasing Functions Application of Calculus in Commerce and Economics (Set I) Application of Calculus in Commerce and Economics (Set II) Integration MCQs (Set 1)  Integration MCQs (Set 2) Specimen Paper for Semester 1 – 2021 – ISC – Class XII Mathematics Linear Regression

Chapterwise Model Questions   –  Class 12 – Mathematics

Matrices (Set1)

Determinants

ISC   –   Class 12  –  Mathematics  –  Sem 2  –  2022  – Sample Paper                             Sample Paper 1                             Sample Paper 2

ISC – Class 12 –  Mathematics – Sem 1 – 2021 – Sample Paper                          Specimen Paper

ISC- Class 12 – Mathematics – Sem 2 – 2022 – Chapterwise Questions                       Differential Equations (Set 1)                       Differential equations (Set 2)                       Integration                      Probability                      Linear Programming (LPP)

 

Formula             Mathematics Formula and Theorems for Class X Class XI Formula Trigonometry Inverse Trigonometric Functions – Class 12   Differentiation and Limits for Class 11 and 12   Integration for Class 11 and 12    Linear Regression – Class 12- ISC

 

ISC / ICSE  Board Paper ISC  – Class 12 – 2020 – Mathematics Question Paper ISC –  Class 12 – 2019 –  Mathematics Question Paper ISC Class 12 Semester 1- 2021 Mathematics Question Paper with Solution ISC – Class 12 – Semester 2-2022 Mathematics Question Paper with Solution ISC – Class 12 – 2023 Mathematics Question Paper with Solution ICSE – Class 10 – 2020- Mathematics Question Paper  ICSE – Class 10 – 2019 – Mathematics Question Paper ICSE – Class 10 – 2018 – Mathematics Question Paper ICSE – Class 10 – 2019 – Physics Question Paper ICSE – Class 10 – 2018 – Physics Question Paper  ICSE – Class 10 -2020- Mathematics Question Paper– Solutions ICSE – Class 10 – 2023 Mathematics Question Paper – Solutions

Contents – Tapati’s Classes