Worked example 1
Question: A fair die is rolled once. Find the probability of getting a prime number.
Solution: Sample space={1,2,3,4,5,6}; primes are {2,3,5}. Probability=3/6=1/2.
What this chapter covers
Use the classical definition of probability for equally likely outcomes, complements and simple experiments such as coins, dice and cards.
Sample space and event
The sample space lists all possible outcomes. An event is a subset of that space. Count favourable outcomes only after confirming the outcomes are equally likely.
Probability bounds
Probability ranges from 0 (impossible) to 1 (certain). The complement of event E is “not E”; its probability is 1−P(E). A theoretical probability need not match a small experimental sample exactly.
Key formulae: P(E)=number of favourable outcomes ÷ total equally likely outcomes. P(not E)=1−P(E).
Worked examples: CBSE question patterns
These are original practice questions modeled on common board-exam patterns; they are not reproduced past-paper questions.
Worked example 2
Question: Two fair coins are tossed. Find the probability of exactly one head.
Solution: Outcomes={HH,HT,TH,TT}; exactly one head occurs in HT and TH. Probability=2/4=1/2.
Practical activity / investigation
Toss a coin 50 times and record the number of heads. Calculate experimental frequency/50, then compare with theoretical probability 1/2. Repeat in groups and combine the data to see how larger samples often get closer.
Record: Write the aim, materials, steps, observations and conclusion in your notebook. Follow teacher supervision for any classroom activity.
Quick practice with answers
Try each question before opening its solution.
Practice 1: A bag has 5 red and 3 blue balls. Find P(blue) on one random draw.
P(blue)=3/(5+3)=3/8.
Practice 2: Find the probability that a die roll is not a 6.
1−1/6=5/6.
Practice 3: A card is chosen from cards numbered 1 to 10. Find P(number greater than 7).
Favourable numbers are 8,9,10; probability=3/10.
Revision checklist
- Can I explain the key idea without memorising a worked solution?
- Have I selected the right formula and written units where needed?
- Can I show each algebraic or geometric step clearly?
- Can I check my answer by substitution, estimation or a diagram?
Aligned to the Class X Mathematics curriculum for 2026–27 and the NCERT Mathematics textbook. Always confirm any school-specific internal assessment with your teacher.