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Class 10 Probability: 8 practice questions with answers, step by step

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These are 8 practice questions on NCERT Class 10 Maths Chapter 14, Probability, each with a worked answer. They cover the theoretical probability of an event with equally likely outcomes: dice, coins, playing cards, balls in a box, complementary events and two dice thrown together. Give each answer as a fraction in lowest terms. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every answer was re-computed by a test script, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Mathematics, Textbook for Class X, Reprint 2026-27, Chapter 14, printed pages 202 to 217):

One die, one coin, one card

Question 1. A fair die is rolled once. What is the probability that it shows an even number? (As a fraction.)

Answer: 1/2. The even numbers are 2, 4 and 6, which is 3 of the 6 equally likely outcomes, so P = 3/6 = 1/2.

Question 2. A card is picked at random from a full pack of 52 playing cards. What is the probability of getting a king? (As a fraction.)

Answer: 1/13. There are 4 kings among the 52 cards, so P = 4/52 = 1/13. (A deck has 52 cards, page 207.)

Question 3. Two coins are tossed together. What is the probability of getting exactly one head? (As a fraction.)

Answer: 1/2. The outcomes are HH, HT, TH and TT, all equally likely. Exactly one head happens in 2 of the 4 outcomes (HT and TH), so P = 2/4 = 1/2.

Balls and marbles

Question 4. A box has 5 green, 6 red and 9 yellow balls. One ball is drawn at random. What is the probability that it is not yellow? (As a fraction.)

Answer: 11/20. There are 5 + 6 + 9 = 20 balls, and 5 + 6 = 11 of them are not yellow, so P = 11/20. (Check with complementary events: P(yellow) = 9/20 and 1 − 9/20 = 11/20.)

Question 5. A bag has 5 red, 8 white and 7 green marbles. One marble is taken out at random. What is the probability that it is white? (As a fraction.)

Answer: 2/5. There are 5 + 8 + 7 = 20 marbles and 8 of them are white, so P(white) = 8/20 = 2/5.

Complementary events and limits

Question 6. The probability of an event is 0.35. What is the probability that it does not happen? (As a decimal.)

Answer: 0.65. P(not E) = 1 − P(E) = 1 − 0.35 = 0.65. (Summary, page 217.)

Question 7. A student says the probability of an event is 1.2. Can this be right? Why or why not?

Answer: no. The probability of any event is a number between 0 and 1, that is 0 ≤ P(E) ≤ 1. The number of favourable outcomes can never be more than the number of all possible outcomes, so a probability cannot be 1.2. (Page 207 and summary, page 217.)

Two dice

Question 8. Two dice are thrown at the same time. What is the probability that the sum of the two numbers is 9? (As a fraction.)

Answer: 1/9. There are 6 × 6 = 36 equally likely outcomes (the pair (3, 6) is different from (6, 3)). The pairs with sum 9 are (3, 6), (4, 5), (5, 4) and (6, 3), which is 4 outcomes. So P = 4/36 = 1/9. (The table of 36 outcomes is on page 213; this sum is our own.)

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Sources

All opened and read on 21 October 2026. Page numbers are the printed page numbers of the textbook.

The definitions and rules are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the official CBSE notices.