CBSE Class 11 · Mathematics
Probability
Official NCERT chapter from Mathematics (book code kemh1). ExamMaster notes are original teaching at CBSE Class 11 depth.
This lesson follows the official chapter “Probability” in Mathematics. The words below are ExamMaster’s teaching, not a paste from the book. Use the NCERT chapter for the classroom sequence; use these notes to hold the idea without copying exercises or figures.
- CBSE Class 11
- Medium level
- 8 concepts
1Event
An event is a subset of the sample space S: the outcomes you count as a success. On a fair die, “even” is {2,4,6}. An outcome is one ticket; the event is the bundle. A mood-word with no subset is not an event.
Calling “lucky” an event without listing faces is a heading.
Figure. Each tile is one equally likely draw. Favourable red tiles are 8 of the 14, so P(red) = 8/14.
How it works
- Write SThe whole list.
- Circle the success-ticketsThe event E.
- Keep E ⊆ SA subset.
2Axiomatic Approach to Probability
Axiomatic probability assigns each event a number P(E) with: P ≥ 0, P(S)=1, and additivity for exclusive unions as taught. Equally likely n(E)/n(S) is one model that fits the axioms. An axiom is a rule the assignment must keep, not a vibe of fairness.
Assigning P(even)=2 because you like even is not axiomatic.
Figure. Axioms pin every event on this interval: P(impossible) = 0, P(sure) = 1, and any other event sits strictly between.
How it works
- Check P≥0 and P(S)=1The first rules.
- If E and F share no outcome, P(E∪F)=P(E)+P(F) as taughtAdditivity.
- Use n(E)/n(S) when equally likelyA model that fits.
Even on a fair die, axiomatic check
S has 6 faces. E={2,4,6}. Check P(E)+P(E′)=1.
- P(E)3/6=1/2
- P(E′)1/2
- Sum1 = P(S)
Pro tip. Complements add to 1; the axioms hold.
3A definition is a test you can run
Event / P is a test: a subset plus a number in [0,1] that respects the axioms. If you only say “chance”, you have a heading.
A lottery advert is not the test.
Figure. The school test is count-then-divide: six red tiles over ten equally likely tiles gives P(red) = 6/10.
How it works
- Name S and EThe object.
- Give P(E) from the modelThe test.
- Then the word has contentThe definition ran.
4Name the given before the unknown
The given is the trial and the success-words. The unknown is E or P(E). Copy S before you drop a face.
Calling a die “even” and listing {2,4} only is a silent given.
Figure. Write the given counts before the unknown: 6 red and 4 blue make a total of 10, so the unknown P(red) is 6/10.
How it works
- Copy the trial and the wordsThe given.
- Name E or PThe unknown.
- Then list and countGiven first.
5One worked case is enough at this class
One event-and-share is enough. A page of the same 3/6 clone does not add a new axiom-check.
Ten twins of 1/2 are still one idea.
Figure. One bag: 5 red and 3 blue, eight equally likely draws. The bars are the counts; P(red) = 5/8.
How it works
- Run one E and one PThe case.
- A second only as a checkOptional.
- StopThis class.
6A miss: swapping the school name for the picture
A cricket-photo is a setting. The maths is S and a subset. A cheer is not P(E).
A stadium still is not an axiom.
Figure. The miss is treating the word red as one outcome. The picture that matches the bag is eight equally likely red draws, not one labelled box.
How it works
- Keep the match as a storyA setting.
- Write S and EThe maths.
- Then PDo not swap.
7Check by the opposite action or the opposite test
Check P by the complement (must add to 1) or by recounting E. Exclusive additivity fails if you add overlapping events raw.
Adding P(even)+P(prime) on a die without unpacking 2,3,5 double-counts.
Figure. Check by the complement: P(red) + P(not red) = 1. Eight red and six not-red tiles fill the fourteen draws.
How it works
- State 1/2 or P(E∪F)The claim.
- Use 1−P or list the unionThe check.
- Mend if they disagreeHonest.
8Keep the claim at this chapter, not the next
This chapter’s claim stops at events and the axiom-rules (plus equally likely as a model). It does not steal a random-variable dump, and it does not start Class 12 Bayes unless that is official later.
A page that already “does distributions” here misses the next official idea.
Figure. Stay with a finite equally-likely list. A dependence or Bayes tree is a later chapter — do not invent it here.
How it works
- Keep E ⊆ S and the three rulesThis chapter.
- Leave later official probability for those chaptersThe next map.
- Do not treat the map as already answeredClaim-size.
An event is
- A subset of S — a bundle of outcomes
- One mood-word
- Always S itself
Tickets in a bundle.
Notes
- The official chapter title is “Probability”. Teach the school test for that title, not a contest shortcut.
- If a step needs a later class, stop. The next official chapter will pick it up.
Formulas
- E ⊆ S
- 0 ≤ P(E) ≤ 1, P(S)=1
- exclusive: P(E∪F)=P(E)+P(F)
Recap
Hold these pegs from the official chapter “Probability”. The wording is ExamMaster’s teaching, not a textbook recap.
- Event
- An event is a subset of the sample space S: the outcomes you count as a success.
- Axiomatic Approach to Probability
- Axiomatic probability assigns each event a number P(E) with: P ≥ 0, P(S)=1, and additivity for exclusive unions as taught.
- A definition is a test you can run
- Event / P is a test: a subset plus a number in [0,1] that respects the axioms.
- Name the given before the unknown
- The given is the trial and the success-words.
- One worked case is enough at this class
- One event-and-share is enough. A page of the same 3/6 clone does not add a new axiom-check.
- A miss: swapping the school name for the picture
- A cricket-photo is a setting. The maths is S and a subset. A cheer is not P(E).
Practise Probability
Reading is free and needs no account. Practice, mocks and progress live in the app.
- A 4-question practice set that ends the chapter
- 1 quick check with worked explanations
- Timed mocks scored with the real marking scheme
- Readiness tracked per topic, kept on your device