Probability — Class 10 Maharashtra SSC Mathematics revision notes
A 4-page visual revision sheet for Probability, written for Class 10 Maharashtra SSC 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
counting the favourable cases against all the equally likely ones, and the traps in the counting
The vocabulary, fixed before anything else
- a random experiment has more than one possible result and none of them can be predicted with certainty
- the sample space S is the set of every possible outcome, and n(S) is how many there are
- an event A is any subset of the sample space, and n(A) is the count of outcomes favourable to it
- outcomes must be equally likely for the formula below to apply, which is why we speak of a fair coin and an unbiased die
- an elementary event has exactly one outcome, and a certain event is the whole sample space
- two events are mutually exclusive when they cannot both happen, such as a die showing 2 and showing 5 on one throw
The results this chapter needs
- probability of an event
P(A) = n(A)/n(S) - the range every probability lies in
0 ≤ P(A) ≤ 1 - the complement, A not happening
P(A) = 1 - P(A) - all elementary probabilities add to one
Σ P = 1 - an impossible event, then a certain one
P = 0,quad P = 1
The standard sample spaces, worth knowing cold
| Experiment | n(S) | Worth remembering |
|---|---|---|
| one coin | 2 | H, T |
| two coins | 4 | HH, HT, TH, TT |
| three coins | 8 | 2 × 2 × 2 |
| one die | 6 | 1 to 6 |
| two dice | 36 | ordered pairs, 6 × 6 |
| a pack of cards | 52 | 4 suits of 13 |
The pack of cards, in the detail questions use
- 52 cards in four suits of 13 each: spades, clubs, hearts and diamonds
- spades and clubs are black, hearts and diamonds are red, so 26 of each colour
- each suit runs ace, 2 to 10, then jack, queen and king, so there are 4 of every rank
- the face cards are jack, queen and king, giving 3 per suit and 12 in the pack
- an ace is not a face card, which is a distinction questions deliberately test
- so there are 12 face cards, 6 of them red, and 16 cards that are either an ace or a face card
Page 1 of 4. The full sheet, all 4 pages, opens free in the app.
What this Probability sheet covers
- Random experiment
- Sample space
- Event
- The vocabulary, fixed before anything else
- The results this chapter needs
- probability of an event
- the range every probability lies in
- the complement, A not happening
- all elementary probabilities add to one
- an impossible event, then a certain one
- The standard sample spaces, worth knowing cold
- The pack of cards, in the detail questions use
- Two dice, where the counting matters
- Using the complement to save work
- When the complement is the shorter route
- Reading the wording exactly
- Two ways of counting an or
- Mutually exclusive
- Overlapping
- Terms in this chapter
- 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.