Probability (Baye's Theorem)- Previous Years Board Questions with Solutions - ISC- Class 12-Mathematics

Spread the love

Probability (Baye’s Theorem)- Previous Years Board Questions (2000 to Sem 2- 2022) with Solutions – ISC – Class 12- Mathematics

BAYE’S THEOREM

Let S be the sample space and $E_{1}, \, E_{2},\, ....,\, E_{n}$ be n mutually exclusive and exhaustive events associated with a random experiment. If A is any event which occurs with $E_{1} \, or\, E_{2}\, or\, ...\, or\, E_{n},$ then

$P(E_{i}/A)=\frac{P(A\bigcap E_{i})}{P(A\bigcap E_{1})+P(A\bigcap E_{2})+\, ....\, +P(A\bigcap E_{n})}$

$or\, \, P(E_{i}/A)=\frac{P(E_{i})\, \, P(A/E_{i})}{P(E_{1})P(A/E_{1})+P(E_{2})P(A/E_{2})+\, ...\, +P(E_{n})P(A/E_{n})}$

Procedure :

(i) First identify mutually exclusive and exhaustive events $E_{1},\, E_{2},\, ....,\, E_{n}.$

(ii) Then find $P(E_{1}),\, P(E_{2}),\, ...,\, P(E_{n})$ and check whether the sum of these probabilities is 1.

(iii) Identify the event A and find $P(A/E_{1}),\, P(A/E_{2}),\, ....,\, P(A/E_{n}).$

(iv) Calculate $P(E_{i}/A)$ by using Baye’s Theorem.

S Probability (Bayes Theorem) 1 S Probability (Bayes Theorem) 2 S Probability (Bayes Theorem) 3 S Probability (Bayes Theorem) 4 S Probability (Bayes Theorem) 5 S Probability (Bayes Theorem) 6 S Probability (Bayes Theorem) 7 XII M B Q S Probability (Baye's Theorem) 2000 to Sem 2-2022 (8)

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)