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MathematicsClass 9What is Probability?

What is Probability? | Class 9 Mathematics Notes

By ConceptScroll Team · Published on 17 July 2026 · 5 min read

What is Probability? – this guide gives you a concise, exam-ready overview of What is Probability? from Class 9 Mathematics, written by ConceptScroll editors and reviewed against the latest NCERT textbook.

7.1.2 The Probability Scale

Probability is measured on a scale from 0 to 1, where 0 indicates an impossible event and 1 indicates a certain event. Values between 0 and 1 express varying degrees of likelihood. For example, if the probability of your school winning a hockey match is 0.75, it means there is a 75% chance of winning, so the event is more likely than not. If the probability is 0.5, it means the event is equally likely to happen or not happen. A probability of 0 means the event cannot occur, while a probability of 1 means the event is guaranteed.

The probability scale helps compare how likely different events are. For example, in a deck of six cards with an unknown number of purple and green cards, the probability of picking a purple card ranges from 0 (if no purple cards are present) to 1 (if all cards are purple). As the number of purple cards increases, the probability moves smoothly along the scale from impossible to certain.

Examples of events and their probabilities on the scale include:

  • Getting a number greater than 6 on a die: impossible (probability 0)
  • Rolling a 3 on a die: less likely (probability 1/6)
  • Flipping a coin and getting heads: even chance (probability 1/2)
  • Drawing a number from 2 to 10 in a deck of cards: more likely (probability greater than 1/2)
  • Choosing a red sweet from a bag of all red sweets: certain (probability 1)

This scale allows us to express and understand the likelihood of events in a clear, numerical way.

📊 Diagram: Figure 7.1 shows a probability scale from 0 to 1 with examples of picking purple cards from a deck varying from no purple cards (probability 0) to all purple cards (probability 1).

🧪 Activity: Think and Reflect: Rank events such as 'next Monday comes after Sunday' or 'it will snow in Mumbai in July' on the probability scale from impossible to certain.

🔗 Connection: Understanding the probability scale leads to learning how to measure probability objectively through experiments and theoretical calculations.

Frequently asked questions

Rank the following events on a scale from 0 (Impossible) to 1 (Certain). Label each event: Impossible, less likely, equally likely (even chance), more likely, certain. Give reasons why you gave each event its ranking. (i) The next Monday will come after Sunday. (ii) It will snow in Mumbai in July. (iii) An elephant will walk through your classroom today. (iv) You will greet at least one friend at school tomorrow.

Solution:

(i) The next Monday will come after Sunday.

  • This event is certain because Monday always follows Sunday.
  • Probability = 1 (Certain)

(ii) It will snow in Mumbai in July.

  • Mumbai has a tropical climate and it never snows there.
  • Probability = 0 (Impossible)

(iii) An elephant will walk through your classroom today.

  • This is highly unlikely and practically impossible in normal circumstances.
  • Probability = 0 (Impossible)

(iv) You will greet at least one friend at school tomorrow.

1. A teacher mixes a large bag of sweets of different colours and randomly selects a sample of 30 sweets. She counts the number of sweets of each colour: 10 red sweets | 8 green sweets | 7 yellow sweets | 5 blue sweets (i) Calculate the probability that a randomly picked sweet from the sample is green. (ii) If there are 600 sweets in total in the large bag, estimate how many are likely to be yellow, based on the sample results.

(i) Total sweets in sample = 30 Number of green sweets = 8 Probability (green) = Number of green sweets / Total sweets = 8/30 = 4/15

(ii) Total sweets in large bag = 600 Proportion of yellow sweets in sample = 7/30 Estimated number of yellow sweets in large bag = (7/30) × 600 = 140 sweets

2. A survey is conducted at a school where a random sample of 40 students is asked about their favourite club. The responses are: 14 students: Science Club | 11 students: Arts Club | 9 students: Sports Club | 6 students: Debate Club Assume there are 800 students in the whole school. (i) What is the probability that a randomly chosen student from the sample prefers the Arts Club? (ii) Using the sample results, estimate how many students in the whole school are likely to prefer the Sports Club.

(i) Total students in sample = 40 Number preferring Arts Club = 11 Probability (Arts Club) = 11/40

(ii) Total students in school = 800 Proportion preferring Sports Club in sample = 9/40 Estimated number preferring Sports Club in school = (9/40) × 800 = 180 students

3. Toss a coin 20 times and record the result each time (heads or tails). (i) How many times did you get heads? (ii) How many times did you get tails? (iii) Calculate the experimental probability of getting heads. (iv) If you toss the coin once more, what is the probability of getting tails?

(i) Count the number of heads obtained in 20 tosses. (ii) Count the number of tails obtained in 20 tosses. (iii) Experimental probability of heads = (Number of heads) / 20 (iv) Probability of tails in a fair coin toss = 1/2

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