Probability
Class 11 · Mathematics
4 ideas in Class 11 Mathematics, explained in plain words, with games and quizzes to practise.
Random Experiments and Sample Spaces
Part of: Experiments and Events
Repeatable uncertain trials form random experiments; all outcomes gather in sample spaces; coins multiply by two, dice by six; equally likely means symmetric.
Why it matters. Sample spaces frame every probability. Counting outcomes sets denominators.
Formulas
- One coin: 2 outcomes, one die: 6 outcomes
- Two coins: 2 x 2 = 4 outcomes; two dice: 6 x 6 = 36 outcomes
Key words
- Random experiment
- : A repeatable trial whose outcome is uncertain, as tossing a coin.
- Outcome
- : One possible result of a random experiment.
- Sample space
- : The set of all possible outcomes of an experiment.
- Equally likely
- : Outcomes with symmetric chances, so each gets a fair share of probability.
Try it in two minutes
- Name the trial.
- List all outcomes.
- Count them.
Try at home. List two-coin outcomes.
Types of Events
Part of: Experiments and Events
Empty set marks impossible, full space sure; complements negate; simple holds one outcome, compound many; mutually exclusive never overlap; exhaustive cover all.
Why it matters. Event types unlock formulas. Overlap decides addition.
Formulas
- Impossible event = empty set
- Sure event = whole sample space
Key words
- Impossible event
- : The empty set, with no outcome and probability zero.
- Sure event
- : The whole sample space, certain to happen with probability one.
- Complement
- : The event of everything outside E, written as not E.
- Simple event
- : An event holding exactly one outcome of the sample space.
- Mutually exclusive
- : Two events that never overlap, sharing no outcome.
- Exhaustive events
- : Events that together cover every outcome of the sample space.
Try it in two minutes
- Subset the sample space.
- Check overlap.
- Complement for opposites.
Try at home. Classify die events.
Axiomatic Probability
Part of: Probability Rules
Probabilities sit between zero and one; whole space totals one; disjoint unions add; equally likely divides favourables by totals; complements subtract from one.
Why it matters. Axioms ground every computation. Complements shortcut opposites.
Formulas
- 0 <= P(E) <= 1
- P(S) = 1 for the whole sample space
- P(not E) = 1 - P(E)
- P(E) = n(E) / n(S) for equally likely outcomes
Key words
- Probability
- : A number from 0 to 1 measuring how likely an event is.
- Axiom
- : A starting rule of probability from which the other rules follow.
- Equally likely probability
- : Favourable outcomes divided by total outcomes under symmetry.
- Complement rule
- : The rule that P(not E) = 1 - P(E).
Try it in two minutes
- Bound between zero and one.
- Count favourables over totals.
- Subtract for opposites.
Try at home. Compute die-face chances.
Addition Theorem and Applications
Part of: Probability Rules
Disjoint unions add directly; overlapping unions subtract the intersection; exhaustive disjoint events total one; odds convert ratios to shares.
Why it matters. Overlap correction prevents double count. Exhaustion checks completeness.
Formulas
- P(A union B) = P(A) + P(B) - P(A and B)
- Mutually exclusive: P(A union B) = P(A) + P(B)
Key words
- Union of events
- : The event that A or B or both happen.
- Intersection of events
- : The event that A and B happen together.
- Addition theorem
- : The rule adding two probabilities and removing the overlap once.
- Odds
- : A ratio form of chance that converts to shares of the total.
Try it in two minutes
- Check disjoint or overlap.
- Add, subtract if shared.
- Verify totals.
Try at home. Compute P(even or over 4).
What your child will practise
- Addition Theorem and Applications: Candy Puzzle (Clue Puzzle)
- Addition Theorem and Applications: Candy Quick Fire (Quick Fire)
- Axiomatic Probability: Desert Puzzle (Clue Puzzle)
- Random Experiments and Sample Spaces: Ocean Quest (Flip and Match)
- Types of Events: Ocean Quick Fire (Quick Fire)
- Quiz: Addition Theorem and Applications (8 questions)
- Quiz: Axiomatic Probability (8 questions)
- Quiz: Random Experiments and Sample Spaces (8 questions)
- Quiz: Types of Events (8 questions)