Imagine pulling a random card from a deck and guessing the chance it’s a heart – that tiny thrill is exactly what probability lets you measure.
💡 In Simple Words: Probability tells you how likely something is to happen. If you have 2 red marbles and 8 blue ones, the chance of picking a red marble is 2 out of 10, or 2/10.
Probability formula for ICSE Class 10
The basic formula is:
Probability (P) = Number of favourable outcomes ÷ Total number of possible outcomes
“Favourable outcomes” are the ways you want the event to happen. “Possible outcomes” are every way anything could happen.
Why the formula works – a water‑pipe analogy
Think of the total outcomes as the whole width of a pipe. The favourable outcomes are a smaller channel inside that pipe. The bigger the channel, the more water (or chances) can flow through.
Common types of probability questions in the board exam
- Finding probability of a single event (e.g., drawing a king from a deck).
- Probability of complementary events – the chance that something doesn’t happen.
- Probability of two independent events happening together (e.g., tossing a coin and rolling a dice).
- Probability in simple word problems (e.g., selecting students for a team).
Step‑by‑step method to solve a probability problem
Follow these four easy steps every time you see a probability question.
Worked example 1: Drawing a vowel from the word “EXAM”
Step 1 – Total outcomes: The word has 4 letters, so 4 possible picks.
Step 2 – Favourable outcomes: Vowels are E and A, so 2 favourable picks.
Step 3 – Apply the formula: P = 2 ÷ 4 = ½.
Step 4 – Answer: The probability of picking a vowel is 0.5 or ½.
Worked example 2: Two‑dice sum of 7
Step 1 – Total outcomes: Each die has 6 faces, so 6 × 6 = 36 possible pairs.
Step 2 – Favourable outcomes: The pairs (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) give a sum of 7 – that’s 6 ways.
Step 3 – Apply the formula: P = 6 ÷ 36 = 1/6.
Step 4 – Answer: The chance of getting a total of 7 is 1⁄6.
Quick summary table
| Situation | Total outcomes | Favourable outcomes | Probability |
|---|---|---|---|
| Single card is a heart (52‑card deck) | 52 | 13 | 13/52 = 1/4 |
| Coin shows heads | 2 | 1 | 1/2 |
| Pick a red marble (2 red, 8 blue) | 10 | 2 | 2/10 = 1/5 |
| Two dice sum = 7 | 36 | 6 | 1/6 |
Tips to avoid common mistakes
- Never forget to count *all* possible outcomes – even the ones that look “impossible”.
- When events are independent, multiply their individual probabilities; don’t add them.
- Reduce fractions at the end – a simplified answer looks cleaner on the answer sheet.
- Check if the question asks for “probability of not happening”; that’s just 1 − P.
📝 Likely Exam Questions
- Question: A bag contains 3 red, 4 green and 5 blue balls. One ball is drawn at random. Find the probability that it is not green.
Answer: Total = 12, favourable (not green) = 3 + 5 = 8, P = 8/12 = 2/3. - Question: Two dice are rolled. What is the probability of getting a total of 9?
Answer: Total outcomes = 36. Favourable pairs: (3,6),(4,5),(5,4),(6,3) → 4 ways. P = 4/36 = 1/9. - Question: From the letters of the word “PROBABILITY”, one letter is chosen at random. Find the probability that the chosen letter is a vowel.
Answer: Word has 11 letters; vowels = O, A, I, I, I → 5 vowels. P = 5/11. - Question: A coin is tossed three times. What is the probability of getting exactly two heads?
Answer: Total outcomes = 2³ = 8. Favourable = 3 ways (HHT, HTH, THH). P = 3/8. - Question: In a class of 40 students, 18 like maths, 12 like science and 5 like both. If a student is chosen at random, find the probability that the student likes either maths or science.
Answer: Using inclusion‑exclusion: Likes maths or science = 18 + 12 − 5 = 25. P = 25/40 = 5/8.