ICSE Class 10 Mathematics Probability: Basic Problems for Exams

Ever wondered why picking a red marble from a bag feels like a mini‑guessing game?

Probability tells us how likely something is to happen. If you have 4 red balls and 6 blue ones, the chance of pulling a red ball is 4 out of 10, or 40%.

What is Probability?

In everyday words, probability measures the chance of an event occurring. Think of it like a weather forecast: a 70% chance of rain means it's more likely than not, but not guaranteed.

Key Terms You Must Know

• Experiment: any action you can repeat, like tossing a coin.
• Outcome: a single result of that experiment, such as "heads".
• Event: a set of one or more outcomes you care about, for example "getting a head or a tail" (that's actually all outcomes).
• Sample space: the complete list of all possible outcomes. For a six‑sided die, it’s {1,2,3,4,5,6}.

How to Find Basic Probability

The basic formula is:

Probability = (Number of favourable outcomes) ÷ (Total number of possible outcomes)

Make sure the outcomes you count are equally likely – each outcome should have the same chance of happening.

Worked Example 1: Rolling a Dice

Question: What is the probability of getting an even number when you roll a fair die?

1. Identify the sample space: {1,2,3,4,5,6} (six possible results).
2. List the favourable outcomes – the even numbers: {2,4,6} (three results).
3. Apply the formula: Probability = 3 ÷ 6 = ½ or 0.5 (50%).

Worked Example 2: Drawing a Card

Question: From a standard 52‑card deck, what is the probability of drawing a heart?

1. Sample space = 52 cards.
2. Favourable outcomes = 13 hearts.
3. Probability = 13 ÷ 52 = ¼ or 0.25 (25%).

Quick Tips for Solving Board Exam Problems

• Always write down the total number of outcomes first – it saves you from missing something.
• If the problem involves “or”, add the probabilities of each separate event (but subtract the overlap if they can happen together).
• For “and” situations, multiply the probabilities of each independent event.
• Check whether the question asks for “at least” or “exactly” – that changes which outcomes you count.
• Keep fractions simple; you can convert to decimals or percentages if the exam asks.

Comparison Table: Common Probability Situations

📝 Likely Exam Questions

1. Question: A bag contains 3 red, 2 blue and 5 green marbles. One marble is drawn at random. What is the probability of getting a blue marble?
   Answer: Total = 10 marbles, favourable = 2 blue. Probability = 2/10 = 1/5 = 0.2 (20%).
2. Question: Two dice are thrown together. Find the probability of obtaining a sum of 7.
   Answer: Possible pairs giving 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6 favourable. Total outcomes = 6×6 = 36. Probability = 6/36 = 1/6 ≈ 0.167.
3. Question: From a deck of 52 cards, two cards are drawn without replacement. What is the probability both are aces?
   Answer: First ace: 4/52. Second ace (after one removed): 3/51. Multiply → (4/52)*(3/51)=12/2652=1/221 ≈ 0.0045 (0.45%).
4. Question: A coin is tossed three times. What is the probability of getting exactly two heads?
   Answer: Number of ways to choose 2 heads out of 3 tosses = C(3,2)=3. Each specific sequence has probability (½)^3 = 1/8. So total = 3*(1/8)=3/8=0.375 (37.5%).
5. Question: In a class of 40 students, 25 like maths, 18 like science, and 10 like both. If a student is chosen at random, what is the probability they like either maths or science?
   Answer: Use “or” formula: P(M ∪ S)=P(M)+P(S)‑P(M∩S). = (25/40)+(18/40)-(10/40)=33/40=0.825 (82.5%).