Complementary events and coins: Class 10 practice

What you should know first

• Fractions

The idea behind complementary events and coins

P(not E) = 1 − P(E). For coin tosses, list the equally likely outcomes (HH, HT, TH, TT for two coins) and count.

Step-by-step method

1. List all equally likely outcomes.
2. Count the favourable ones.
3. Use P(not E) = 1 − P(E) for 'at least' or 'not'.

Worked example 1 (Basic)

A die is thrown once. Find the probability of getting a number at most 1.

1. Outcomes 1–6
2. Favourable = 1
3. P = 1/6
4. Answer: 1/6

Worked example 2 (Standard)

4 coins are tossed. Find the probability of exactly 3 heads.

1. Total outcomes = 2^4 = 16
2. Favourable = 4C3 = 4
3. P = 1/4
4. Answer: 1/4

Worked example 3 (Challenge)

4 coins are tossed. Find the probability of at least one head.

1. P(no head) = 1/16
2. P = 1 − 1/16 = 15/16
3. Answer: 15/16

Common mistakes and misconceptions

• Treating HT and TH as one outcome
• Forgetting 1 − P(E)

Practice questions

1. (Basic) A die is thrown once. Find the probability of getting a number greater than 4.
2. (Basic) A die is thrown once. Find the probability of getting a number at most 3.
3. (Standard) 3 coins are tossed. Find the probability of exactly 3 heads.
4. (Standard) 4 coins are tossed. Find the probability of exactly 2 heads.
5. (Challenge) 2 coins are tossed. Find the probability of at least one head.
6. (Challenge) 3 coins are tossed. Find the probability of at most one head.

Answer key with full working

• Q1: Outcomes 1–6 → Favourable = 2 → P = 1/3 → Answer: 1/3
• Q2: Outcomes 1–6 → Favourable = 3 → P = 1/2 → Answer: 1/2
• Q3: Total outcomes = 2^3 = 8 → Favourable = 3C3 = 1 → P = 1/8 → Answer: 1/8
• Q4: Total outcomes = 2^4 = 16 → Favourable = 4C2 = 6 → P = 3/8 → Answer: 3/8
• Q5: P(no head) = 1/4 → P = 1 − 1/4 = 3/4 → Answer: 3/4
• Q6: 0 heads: 1 way, 1 head: 3 ways → P = 1/2 → Answer: 1/2

Syllabus note

This skill is listed under "Probability" for Class 10 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.

Related practice and notes

• Probability chapter notes (Class 10)
• Probability with dice and cards
• Two dice: sums and doubles
• Solving quadratic equations
• AP nth term and sum
• Distance formula and section formula
• Finding all trigonometric ratios from one
• All Class 10 practice

Frequently asked questions

Which chapter is complementary events and coins in?

"Probability", Class 10 Maths (NCERT/CBSE). Other boards may place it differently.

How were the answers checked?

Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.