Probability (Addition and Multiplication Theorem, Conditional Probability) Previous Years Board Questions with Solutions of ISC Class 12 Mathematics

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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).

p = P(A)= \frac{m}{n}=\frac{\mathrm{no\: of \: favourable \: events}}{\mathrm{toal\: no\: of\: elementary\: events}}

The probability q of failure of event A is

q=P(A\bar{})=1-\frac{m}{n}=1-P(A)=1-p

\therefore P(A)+P(A\bar{})=p+q=1

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)

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

                            Sample Paper 1
                            Sample Paper 2
ISC – Class 12 –  Mathematics – Sem 1 – 2021 – Sample Paper

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ISC- Class 12 – Mathematics – Sem 2 – 2022 – Chapterwise Questions

                      Differential Equations (Set 1)
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                      Integration
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     ISC / ICSE  Board Paper

ISC  – Class 12 – 2020 – Mathematics Question Paper
ISC –  Class 12 – 2019 –  Mathematics Question Paper
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 PaperSolutions

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