Chapter Hub
Probability
Probability tells us how likely an event is to happen, using a number from 0 to 1. For CBSE Class 10, the chapter begins with simple experiments like tossing coins, throwing dice, drawing balls, and selecting cards, then moves to comparing chances and using complements. The main skill is careful counting. You must build the sample space correctly, identify favourable outcomes, and apply the formula only when outcomes are equally likely. Most exam errors come from wrong counting, missing outcomes, or mixing up event and complement.
Difficulty
Medium
Study time
96-120 min
Plan by time
Pick the window that matches what you have right now.
If you have 15 min
Last-pass revision
Skim the Quick Revision table — definitions, formulas, and the traps board examiners reuse.
Open Quick RevisionIf you have 45 min
Targeted practice
Read the high-priority concepts, then take the chapter MCQ quiz to find weak spots.
Start MCQ QuizIf you have 96 min
First full pass
Walk every concept in chapter order, then revise and quiz. Best for the first time you study this chapter.
Open Key ConceptsChapter Learning Map
Start with one of the buckets below, then open the full map when you want the complete concept roadmap.
Core counting ideas
Covers Probability of an event, Probability as favourable over total outcomes and Checking validity of a probability value.
Open mapSample spaces
Covers Equally likely outcomes, Sample space for coin toss and Sample space for die throw.
Open mapSpecial cases
Covers Impossible event, Certain event and Complement of an event.
Open mapApplications
Covers Probability in card selection contexts, Probability in spinner or bag contexts and Comparing likelihood of events.
Open mapKey Concepts
Concepts grouped the way the chapter is taught — open the group that matches what you want to revise.
Core counting ideas
Covers Probability of an event, Probability as favourable over total outcomes and Checking validity of a probability value.
Probability of an event
Probability of an event is a number that shows how likely that event is to happen.
Probability as favourable over total outcomes
For equally likely outcomes, probability of an event equals favourable outcomes divided by total outcomes.
Checking validity of a probability value
A probability value is valid only if it lies between 0 and 1, including both ends.
Sample spaces
Covers Equally likely outcomes, Sample space for coin toss and Sample space for die throw.
Equally likely outcomes
Equally likely outcomes are outcomes that have the same chance of happening in an experiment.
Sample space for coin toss
The sample space for a coin toss is the set of all possible outcomes of that toss.
Sample space for die throw
The sample space for throwing a die once is the set of all possible faces that can appear.
Special cases
Covers Impossible event, Certain event and Complement of an event.
Impossible event
An impossible event is an event that cannot happen in a given experiment.
Certain event
A certain event is an event that must happen in a given experiment.
Complement of an event
The complement of an event is the event that the original event does not happen.
Applications
Covers Probability in card selection contexts, Probability in spinner or bag contexts and Comparing likelihood of events.
Probability in card selection contexts
This is the use of probability when one or more cards are chosen from a deck or a card set.
Probability in spinner or bag contexts
This is probability applied to a spinner or a bag where each sector or item may represent an outcome.
Comparing likelihood of events
Comparing likelihood means deciding which event is more likely by comparing their probabilities.
Exam Intelligence
The traps that cost marks in this chapter, and how its main concepts turn up in the paper.
High Probability Topics
- Probability of an event
- Equally likely outcomes
- Sample space for coin toss
- Sample space for die throw
- Probability as favourable over total outcomes
- Impossible event
- Certain event
- Complement of an event
Common Traps
- Missing outcomes in the sample space, especially for two coin tosses.
- Using favourable outcomes as the denominator instead of total outcomes.
- Forgetting that the complement adds up to 1 with the original event.
- Comparing fractions by numerator only or denominator only.
- Accepting values greater than 1 or less than 0 as probabilities.
How CBSE Asks This Chapter
- Probability of an event
Find the probability of a given event from a clear experiment, often with coins, dice, balls, or cards.
- Equally likely outcomes
Students may be asked to identify whether an experiment is fair or to decide if the outcomes are equally likely.
- Sample space for coin toss
Questions usually ask students to list the sample space or count the total number of outcomes for one or more tosses.
- Sample space for die throw
Students may be asked to write the sample space, count outcomes, or find probability of a numbered face.
Quick Revision
Concept, formula or equation to remember, and the trap that loses marks — in one scannable view.
Remember
P(E) = favourable outcomes / total outcomes, provided the outcomes are equally likely.Trap to avoid
Students sometimes divide by the number of favourable outcomes instead of the total number of outcomes.
Remember
Equal likelihood means each outcome has the same chance, so probability counting can be used directly only then.Trap to avoid
Students sometimes call outcomes equally likely just because there are many outcomes, even when the object is biased.
Remember
For one coin toss, S = {H, T}.Trap to avoid
Students often miss ordered outcomes like HT and TH and write only three outcomes.
Remember
For one standard die throw, S = {1, 2, 3, 4, 5, 6}.Trap to avoid
Students sometimes include 0 or forget one face when writing the sample space.
Probability as favourable over total outcomes
Remember
P(E) = favourable outcomes / total outcomes, when the outcomes are equally likely.Trap to avoid
Students sometimes count favourable outcomes correctly but forget to count the full sample space.
Remember
If an event has no favourable outcomes, then P(E) = 0.Trap to avoid
Students sometimes write a small fraction for an impossible event instead of 0.
Remember
If an event includes every outcome of the sample space, then P(E) = 1.Trap to avoid
Students sometimes think probability 1 means one outcome only, instead of an event that always happens.
Remember
P(not E) = 1 - P(E).Trap to avoid
Students often subtract from the wrong number or confuse the complement with a completely different event.
Probability in card selection contexts
Remember
Probability = favourable cards / total cards, after identifying the exact card group asked.Trap to avoid
Students often confuse a suit with a rank and count too many or too few cards.
Probability in spinner or bag contexts
Remember
Probability = favourable parts or items / total equal parts or total items.Trap to avoid
Students sometimes count colours or sectors without checking whether they are equal in size.
Comparing likelihood of events
Remember
A larger probability means a more likely event; compare the values after simplifying if needed.Trap to avoid
Students sometimes compare only the denominators or only the numerators and ignore the full fraction.
Checking validity of a probability value
Remember
Any probability value must satisfy 0 ≤ P(E) ≤ 1.Trap to avoid
Students sometimes accept an answer without checking whether it lies in the allowed range.
| Concept | Remember | Trap to avoid |
|---|---|---|
| Probability of an event | P(E) = favourable outcomes / total outcomes, provided the outcomes are equally likely. | Students sometimes divide by the number of favourable outcomes instead of the total number of outcomes. |
| Equally likely outcomes | Equal likelihood means each outcome has the same chance, so probability counting can be used directly only then. | Students sometimes call outcomes equally likely just because there are many outcomes, even when the object is biased. |
| Sample space for coin toss | For one coin toss, S = {H, T}. | Students often miss ordered outcomes like HT and TH and write only three outcomes. |
| Sample space for die throw | For one standard die throw, S = {1, 2, 3, 4, 5, 6}. | Students sometimes include 0 or forget one face when writing the sample space. |
| Probability as favourable over total outcomes | P(E) = favourable outcomes / total outcomes, when the outcomes are equally likely. | Students sometimes count favourable outcomes correctly but forget to count the full sample space. |
| Impossible event | If an event has no favourable outcomes, then P(E) = 0. | Students sometimes write a small fraction for an impossible event instead of 0. |
| Certain event | If an event includes every outcome of the sample space, then P(E) = 1. | Students sometimes think probability 1 means one outcome only, instead of an event that always happens. |
| Complement of an event | P(not E) = 1 - P(E). | Students often subtract from the wrong number or confuse the complement with a completely different event. |
| Probability in card selection contexts | Probability = favourable cards / total cards, after identifying the exact card group asked. | Students often confuse a suit with a rank and count too many or too few cards. |
| Probability in spinner or bag contexts | Probability = favourable parts or items / total equal parts or total items. | Students sometimes count colours or sectors without checking whether they are equal in size. |
| Comparing likelihood of events | A larger probability means a more likely event; compare the values after simplifying if needed. | Students sometimes compare only the denominators or only the numerators and ignore the full fraction. |
| Checking validity of a probability value | Any probability value must satisfy 0 ≤ P(E) ≤ 1. | Students sometimes accept an answer without checking whether it lies in the allowed range. |
Practice
Use short concept checks first, then move into the full chapter test.
Free Chapter MCQ Quiz
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