Class 10 / Maths
Class 10 Maths Probability Notes
Notes on theoretical probability, outcomes, events, complementary events, dice, coins, and cards.
Topic introduction
Probability in Class 10 is based on simple experiments with equally likely outcomes. The safest method is to write the total outcomes first, count favourable outcomes second, and keep the final answer between 0 and 1.
Key points
- Probability of an event = number of favourable outcomes / total number of equally likely outcomes.
- Probability is always between 0 and 1.
- The probability of a sure event is 1 and the probability of an impossible event is 0.
- For complementary events, P(E) + P(not E) = 1.
Definitions
Outcome: A possible result of an experiment.
Event: A collection of one or more favourable outcomes.
Sample space: The set of all possible outcomes.
Complementary event: The event that E does not occur.
Formulas
- P(E) = favourable outcomes / total equally likely outcomes
- 0 <= P(E) <= 1
- P(not E) = 1 - P(E)
- P(sure event) = 1 and P(impossible event) = 0
Examples
- Probability of head in one fair coin toss is 1/2.
- Probability of an even number on a fair die is 3/6 = 1/2.
- If P(E) = 3/8, then P(not E) = 5/8.
Equally likely outcomes
Use the basic probability formula only when outcomes are equally likely.
For a fair coin, outcomes are head and tail. For a fair die, outcomes are 1, 2, 3, 4, 5, and 6.
Common experiments
Dice, coins, cards, and numbered balls are common board-style probability contexts.
Write the sample space or count outcomes carefully before calculating probability.
Common mistakes
- Counting total outcomes incorrectly.
- Using the formula when outcomes are not equally likely.
- Writing probability greater than 1.
- Forgetting to simplify fractions where useful.
- Confusing favourable outcomes with total outcomes.
Quick practice
- Find the probability of getting a head when one coin is tossed.
- Find the probability of getting an even number on a die.
- Find the probability of drawing a red card from a standard deck.
- If P(E) = 0.35, find P(not E).
Related practice
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