Class 12 Mathematics Chapter 13 Probability – Revision Notes

Probability in this chapter builds from conditional probability up to Bayes’ theorem and the binomial distribution, tying together how earlier events shape the likelihood of later ones.

Last Updated: September 23, 2026

Key Formulas

• Conditional: P(A|B)=P(A∩B)/P(B).
• Multiplication: P(A∩B)=P(A)P(B|A).
• Independence: P(A∩B)=P(A)P(B).

Bayes & Distributions

• Total probability: P(A)=ΣP(E_i)P(A|E_i).
• Bayes theorem: P(E_i|A)=[P(E_i)P(A|E_i)]/ΣP(E_j)P(A|E_j).
• Binomial: P(X=r)=ⁿC_rp^rq^n−r.
• Mean=Σx_ip_i; Variance=E(X²)−[E(X)]².

One-Line Summary

Probability in Class 12 builds on conditional probability and independence to Bayes theorem for reversing conditioning, and to random variables/binomial distributions for modeling repeated trials.

Quick visual: a worked diagram from the full Solutions page, for reference.

Frequently Asked Questions

What is conditional probability, and how is it different from ordinary probability?
Conditional probability is the probability of an event occurring given that another event has already occurred, which narrows the sample space to only the outcomes consistent with the given condition, unlike ordinary probability calculated over the full sample space.

What does Bayes Theorem help calculate?
Bayes Theorem helps calculate the probability of a cause given an observed effect, by reversing conditional probabilities using known prior probabilities, and it is widely used in situations involving multiple possible causes for an outcome.

Written by Satish

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