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Probability

Uttar Pradesh Board · Class 12 · Mathematics

Quick revision notes for Probability — Uttar Pradesh Board Class 12 Mathematics. Key concepts, formulas, and definitions for last-minute revision.

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A Venn diagram illustrating a partition of a sample space S into several pairwise disjoint and exhaustive events E1, E2, ..., En.
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Key Topics to Revise

1

Conditional Probability

  • Conditional probability measures the likelihood of an event occurring given that another event has already occurred
  • Denoted as P(E|F), read as 'probability of E given F'
  • The sample space effectively reduces to the given event when calculating conditional probability
2

Properties of Conditional Probability

  • P(S|F) = P(F|F) = 1, where S is the sample space
  • Addition rule: P((A∪B)|F) = P(A|F) + P(B|F) - P((A∩B)|F)
  • For disjoint events A and B: P((A∪B)|F) = P(A|F) + P(B|F)
3

Multiplication Theorem on Probability

  • Used to find probability of simultaneous occurrence of two events (E∩F)
  • Derived directly from the definition of conditional probability
  • Can be expressed in two equivalent forms depending on which event is conditioned
4

Independent Events

  • Two events are independent if occurrence of one doesn't affect probability of the other
  • For independent events: P(E|F) = P(E) and P(F|E) = P(F)
  • Independence is defined using multiplication: P(E∩F) = P(E)·P(F)

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Full Notes

Key Concepts

The probability of an event EStates that P(E∩F) = P(E) ×Two events E and FA collection of events E₁If E₁

Frequently Asked Questions

What are the important topics in Probability for Uttar Pradesh Board Class 12 Mathematics?
Probability covers several key topics that are frequently asked in Uttar Pradesh Board Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Probability — Uttar Pradesh Board Class 12 Mathematics?
Start by understanding all key concepts. Practise previous year questions from this chapter. Revise formulas and definitions regularly. Use flashcards for quick revision before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

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