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Probability with dice and cards: Class 10 practice

For equally likely outcomes, P(event) = favourable outcomes ÷ total outcomes. Read the method, follow the three worked examples, then try the six questions.

What you should know first

  • Fractions

The idea behind probability with dice and cards

For equally likely outcomes, P(event) = favourable outcomes ÷ total outcomes. It is always between 0 and 1, and P(not E) = 1 − P(E).

Step-by-step method

  1. List or count the total outcomes (6 for a die, 36 for two dice, 52 for cards).
  2. Count favourable outcomes.
  3. Divide and simplify.

Worked example 1 (Basic)

A die is thrown once. Find the probability of getting a number greater than 1.

  1. Favourable: 2, 3, 4, 5, 6 → 5
  2. P = 5/6 = 5/6
  3. Answer: 5/6

Worked example 2 (Standard)

Two dice are thrown together. Find the probability that the sum is 3.

  1. Total outcomes = 36
  2. Pairs with sum 3: 2
  3. P = 2/36 = 1/18
  4. Answer: 1/18

Worked example 3 (Challenge)

One card is drawn from a well-shuffled deck of 52. Find the probability of getting a black card that is a number 2–10.

  1. Favourable outcomes = 18
  2. P = 18/52 = 9/26
  3. Answer: 9/26

Common mistakes and misconceptions

  • Counting (2, 3) and (3, 2) as one outcome for two dice
  • Forgetting a deck has 26 red cards incl. red face cards

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 greater than 5.
  3. (Standard) Two dice are thrown together. Find the probability that the sum is 9.
  4. (Standard) Two dice are thrown together. Find the probability that the sum is 5.
  5. (Challenge) One card is drawn from a well-shuffled deck of 52. Find the probability of getting a red face card.
  6. (Challenge) One card is drawn from a well-shuffled deck of 52. Find the probability of getting a spade.

Answer key with full working

  • Q1: Favourable: 5, 6 → 2 → P = 2/6 = 1/3 → Answer: 1/3
  • Q2: Favourable: 6 → 1 → P = 1/6 = 1/6 → Answer: 1/6
  • Q3: Total outcomes = 36 → Pairs with sum 9: 4 → P = 4/36 = 1/9 → Answer: 1/9
  • Q4: Total outcomes = 36 → Pairs with sum 5: 4 → P = 4/36 = 1/9 → Answer: 1/9
  • Q5: Favourable outcomes = 6 → P = 6/52 = 3/26 → Answer: 3/26
  • Q6: Favourable outcomes = 13 → P = 13/52 = 1/4 → Answer: 1/4

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

Frequently asked questions

Which chapter is probability with dice and cards 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.

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