OP Malhotra **Bayes Theorem** ISC Class-12 Maths Solutions Ch-19. Step by step Solutions of OP Malhotra SK Gupta, Anubhuti Gangal S.Chand ISC Class-12 Mathematics with Exe-19 and Self Revision. Visit official Website CISCE for detail information about ISC Board Class-12 Mathematics.

## OP Malhotra Bayes Theorem ISC Class-12 Maths Solutions Ch-19

Class: | 12th |

Subject: | Mathematics |

Chapter : | Ch-19 Bayes Theorem of Section -A |

Board | ISC |

Writer | OP Malhotra, SK Gupta, Anubhuti Gangal |

Publications | S.Chand Publications 2020-21 |

**-: Included Topics :- **

Exe-19

Self Revision

### OP Malhotra Bayes Theorem ISC Class-12 Maths Solutions Ch-19

**Bayes Theorem Statement :-**

Let E_{1}, E_{2},…,E_{n} be a set of events associated with a sample space S, where all the events E_{1}, E_{2},…, E_{n} have nonzero probability of occurrence and they form a partition of S. Let A be any event associated with S, then according to Bayes theorem,

for any k = 1, 2, 3, …., n

**Bayes Theorem Formula :-**

If A and B are two events, then the formula for Bayes theorem is given by:

**P(A|B) = P(A∩B)/P(B)**

Where P(A|B) is the probability of condition when event A is occurring while event B has already occurred.

P(A ∩ B) is the probability of event A and event B

P(B) is the probability of event B

**Bayes Theorem Derivation :-**

Bayes Theorem can be derived for events and random variables separately using the definition of conditional probability and density.

From the definition of conditional probability, Bayes theorem can be derived for events as given below:

P(A|B) = P(A ⋂ B)/ P(B), where P(B) ≠ 0

P(B|A) = P(B ⋂ A)/ P(A), where P(A) ≠ 0

Here, the joint probability P(A ⋂ B) of both events A and B being true such that,

P(B ⋂ A) = P(A ⋂ B)

P(A ⋂ B) = P(A | B) P(B) = P(B | A) P(A)

P(A|B) = [P(B|A) P(A)]/ P(B), where P(B) ≠ 0

** Formula for Bayes theorem :-**

**The formula for Bayes theorem is:**

P(A|B)= [P(B|A). P(A)]/P(B)

Where P(A) and P(B) are the probabilities of events A and B.

P(A|B) is the probability of event A given B

P(B|A) is the probability of event B given A.

**Exe-19**

### OP Malhotra Bayes Theorem ISC Class-12 Maths Solutions Ch-19

**Self Revision**

OP Malhotra Bayes Theorem ISC Class-12 Maths Solutions Ch-19

**-: End of Bayes Theorem ****S. Chand ISC Class-12 Maths Solution :-**

Return to :- OP Malhotra S. Chand ISC Class-12 Maths Solutions

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