Probability — Class 12 CBSE Mathematics revision notes
A 3-page visual revision sheet for Probability, written for Class 12 CBSE Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
Page 1 as PDF
Probability in one look
once one event is known, the sample space itself shrinks down to it
Conditional probability
- probability of A, given B has already happened
P(A|B) = P(Acap B)/P(B) - defined only when
P(B) > 0 - the symmetric version
P(B|A) = P(Acap B)/P(A), P(A)>0
Multiplication theorem
- for two events
P(Acap B) = P(A) P(B|A) = P(B) P(A|B) - extended to three events
P(Acap Bcap C) = P(A) P(B|A) P(C|Acap B)
Independent vs mutually exclusive
- P(Acap B) = P(A) P(B)
- knowing one happened changes nothing about the other's chance
- A and B share no outcomes, so P(Acap B) = 0
- if both have nonzero probability, knowing one happened rules the other out completely
Page 1 of 3. The full sheet, all 3 pages, opens free in the app.
What this Probability sheet covers
- Reading two events on one diagram
- Conditional probability
- probability of A, given B has already happened
- defined only when
- the symmetric version
- Multiplication theorem
- for two events
- extended to three events
- Independent vs mutually exclusive
- Independent events
- Mutually exclusive events
- Three events sharing one sample space
- Total probability and Bayes' theorem
- E_1,…,E_n must be a genuine partition of the sample space
- law of total probability
- Bayes' theorem
- Applying Bayes' theorem
- Which rule do you need?
- Random variables and their spread
- Things to remember before the traps
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Probability the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.