Probability
About 6 min · Numerical Ability · English
Time worked out from the lesson's 318 words at 150 words a minute, plus a minute for each question.
Probability measures how likely an event is to occur, expressed as a number between 0 (impossible) and 1 (certain). Questions are calculation-light but concept-dependent; a clear understanding of basic definitions gets you quick marks.
Key ideas
- Experiment and Outcome: An experiment is any action with uncertain results (tossing a coin). Each possible result is an outcome (Head or Tail).
- Sample Space (S): The set of all possible outcomes. For one die, S = {1, 2, 3, 4, 5, 6}, so n(S) = 6.
- Event (E): A subset of the sample space that we care about. "Getting an even number" means E = {2, 4, 6}.
- Favourable Outcomes: Outcomes that satisfy the event condition. Count them carefully.
- Probability Range: Always between 0 and 1 inclusive. If your answer exceeds 1 or is negative, recheck immediately.
Watch out for
- Wrong thinking: Forgetting to add all categories in a bag problem
- Correct fix: Always write Total = (count each type) and add before calculating
- Wrong thinking: Adding probabilities when events happen together
Quick reference
- P(E) = Favourable / Total — the only formula you truly need
- Die: 6 outcomes; primes = {2, 3, 5}; evens = {2, 4, 6}
- 2 Coins: 4 outcomes — HH, HT, TH, TT
- Deck of 52: 4 suits × 13 cards; 12 face cards; 4 aces
- Complement shortcut: P(at least one) = 1 − P(none)
Check yourself: 3 questions
1. A bag contains 5 red balls, 4 blue balls, and 3 green balls. If one ball is drawn at random from the bag, what is the probability that it is either red or green?
2. Two dice are thrown simultaneously. What is the probability that the sum of the numbers on the two dice is 7?
3. A box contains 6 white balls and 4 black balls. If two balls are drawn at random one after another without replacement, what is the probability that both balls are white?
This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.
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