Probability — Class 10 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Probability" — 9 important questions with detailed answers for CBSE board exam preparation.

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TL;DR: Free step-by-step NCERT solutions for Class 10 Mathematics chapter "Probability" — 9 important questions with detailed answers for CBSE board exam pre…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

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Key Questions Covered:

A fair die is thrown once. What is the probability of getting a number greate…
Two fair dice are thrown simultaneously. Find the probability of getting a su…
A bag contains 5 red balls, 3 blue balls, and 2 green balls. A ball is drawn …
A card is drawn from a standard deck of 52 playing cards. What is the probabi…
A bag contains 4 red balls and 6 white balls. Two balls are drawn one after t…
Three coins are tossed simultaneously. What is the probability of getting at …
+ 3 more questions in the full chapter

Solutions Summary:

Question	Status
A fair die is thrown once. What is the probability of get…	✓ Solved
Two fair dice are thrown simultaneously. Find the probabi…	✓ Solved
A bag contains 5 red balls, 3 blue balls, and 2 green bal…	✓ Solved
A card is drawn from a standard deck of 52 playing cards.…	✓ Solved
A bag contains 4 red balls and 6 white balls. Two balls a…	✓ Solved
Three coins are tossed simultaneously. What is the probab…	✓ Solved

Showing 6 of 9 questions

Q1: A fair die is thrown once. What is the probability of getting a number greater than 4?

Step 1: Total possible outcomes when a die is thrown = {1, 2, 3, 4, 5, 6} = 6 Step 2: Favorable outcomes (number > 4) = {5, 6} = 2 Step 3: Probability = Favorable outcomes / Total outcomes Step 4: P(number > 4) = 2/6 = 1/3 Final Answer: Probability = 1/3 or approximately 0.333

Q2: Two fair dice are thrown simultaneously. Find the probability of getting a sum of 7.

Step 1: Total possible outcomes when two dice are thrown = 6 × 6 = 36 Step 2: Favorable outcomes (sum = 7): (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) Step 3: Number of favorable outcomes = 6 Step 4: Probability = 6/36 = 1/6 Final Answer: Probability = 1/6 or approximately 0.167

Q3: A bag contains 5 red balls, 3 blue balls, and 2 green balls. A ball is drawn at random. What is the probability of drawing a blue ball?

Step 1: Total number of balls = 5 + 3 + 2 = 10 Step 2: Number of blue balls = 3 Step 3: Probability = Number of blue balls / Total number of balls Step 4: P(blue) = 3/10 Final Answer: Probability = 3/10 or 0.3

Q4: A card is drawn from a standard deck of 52 playing cards. What is the probability of drawing a face card (Jack, Queen, or King)?

Step 1: Total number of cards = 52 Step 2: Number of face cards in a deck: Jacks: 4 (one of each suit) Queens: 4 (one of each suit) Kings: 4 (one of each suit) Total face cards = 4 + 4 + 4 = 12 Step 3: Probability = Favorable outcomes / Total outcomes Step 4: P(face card) = 12/52 = 3/13 Final Answer: Probability = 3/13 or approximately 0.231

Q5: A bag contains 4 red balls and 6 white balls. Two balls are drawn one after the other without replacement. Find the probability that both are red.

Step 1: Total number of balls = 4 + 6 = 10 Step 2: Probability of first ball being red = 4/10 Step 3: After drawing one red ball, remaining balls = 9 Step 4: Remaining red balls = 3 Step 5: Probability of second ball being red = 3/9 Step 6: Since both events are dependent: P(both red) = P(first red) × P(second red | first red) P(both red) = (4/10) × (3/9) Step 7: P(both red) = 12/90 = 2/15 Final Answer: Probability = 2/15 or approximately 0.133

Q6: Three coins are tossed simultaneously. What is the probability of getting at least one tail?

Step 1: Total possible outcomes = 2³ = 8 Step 2: All possible outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, TTT Step 3: Method 1 (Direct counting): Favorable outcomes (at least one tail): HHT, HTH, HTT, THH, THT, TTH, TTT = 7 P(at least one tail) = 7/8 Step 4: Method 2 (Complement): P(at least one tail) = 1 - P(no tail) = 1 - P(all heads) P(all heads) = 1/8 P(at least one tail) = 1 - 1/8 = 7/8 Final Answer: Probability = 7/8 or 0.875

Showing 6 of 9 questions. Visit the full page for complete solutions.