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 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.

Previous Years’ Board Questions on Probability (Baye’s Theorem)

have already been uploaded.

The link to the above Board Questions is given below.

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) Matrices (2000 to Sem 1 – 2021) Matrices (2000 to Sem 1-2021) Determinants (2000 to Sem1-2021) Determinants (2000 to Sem1-2021) Differentiation (2000 to Sem 1- 2021) Differentiation (2000 to Sem 1- 2021) 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) Integration (1990 – 2011) Integration (1990 – 2011) Integration (2012 to 2022) Integration (2012 to 2022) Differential Equations (1991 to 2005) Differential Equations (1991 to 2005) Differential Equations (2006 to 2022) Differential Equations (2006 to 2022) 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) Application of Calculus in Commerce and Economics (2005 to Sem 1-2021) Application of Calculus in Commerce and Economics (2005 to Sem 1-2021) Linear Programming (2008 to Sem 2-2022) Linear Programming (2008 to 2022) Linear Regression (2005 to 2013)  Linear Regression – (2005 to 2013)  Linear Regression (2014 to 2022) Linear Regression –  (2014 to 2022)

 

 

Probability (Addition and Multiplication Theorem ) 1

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.

Probability (Addition and Multiplication Theorems) 2

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)

Probability (Addition and Multiplication Theorems) 3

Probability of the occurrence of at least one of the several independent events of a random experiment:

then the probability that at least one of these events must happen is

 

Probability (Addition and Multiplication Theorems) 4 Probability (Addition and Multiplication Theorems) 5 Probability (Addition and Multiplication Theorem ) 6 Probability (Addition and Multiplication Theorem ) 7

Odds:

Probabilities are often expressed

in terms of ‘odds’.

Download ISC Board Questions On Probability(Addition and Multiplication Theorem)

 

ISC              Class 12                   Mathematics Previous Years Board Questions Solutions of Previous years Board Questions Inverse Trigonometric Functions (2000 to 2020) Inverse Trigonometric Functions (2000 to 2020) Matrices (2000 to 2020) Matrices (2000 to 2020) Determinants (2000 to 2020) Determinants (2000 to 2020) Differentiation (2000 to 2020) Differentiation (2000 to 2020) 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 2020) Maxima and Minima (2000 to 2020) Integration (1990 – 2011) Integration (1990 – 2011) Integration (2012 to 2020) Integration (2012 to 2020) Differential Equations (1991 to 2005) Differential Equations (1991 to 2005) Differential Equations (2006 to 2020) Differential Equations (2006 to 2020) Probability (Addition and Multiplication Theorem-Conditional Probability) (1993 to 2020) Probability (Addition and Multiplication Theorem, Conditional Probability) (1993 to 2020) Probability (Baye’s Theorem) (2000 to 2019) Probability (Baye’s Theorem) (2000 to 2019) Probability (Probability distribution and Binomial distribution) (1992 to 2020) Probability (Probability distribution and Binomial distribution) (1992 to 2020) Application of Calculus in Commerce and Economics (2005 to 2020) Application of Calculus in Commerce and Economics (2005 to 2020) Linear Programming (2008 to 2020) Linear Programming (2008 to 2020) Linear Regression (2005 to 2020)

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

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

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

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