Class 10 Maths Test Paper Chapter 14 Probability | GSEB Board | Detailed Solutions & Marking Scheme

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VEDANT CLASSES – A Pathway to Success…

Class: 10
Subject: Maths
Chapter: Probability (Dice, Coins, Cards, Leap Year, At least/At most)
Marks: 30

Section A (7 Marks)

(3 MCQs + 2 Fill in the blanks + 2 True/False)

Q1. MCQs (1 mark each)

  1. A die is thrown once. Find the probability of getting a number greater than 4.
    (A) 1/6 (B) 1/3 (C) 1/2 (D) 2/3

  2. Two coins are tossed. Find the probability of getting exactly one head.
    (A) 1/4 (B) 1/2 (C) 3/4 (D) 1

  3. A card is drawn from a pack of 52 cards. Find probability of getting a red card.
    (A) 1/4 (B) 1/2 (C) 3/4 (D) 13/52

Q2. Fill in the blanks (Choose correct option)

  1. Probability of getting a tail when a coin is tossed = ______ (1/2, 1, 0)

  2. Probability of getting a number less than 7 on a die = ______ (1, 1/2, 1/6)

Q3. True or False

  1. Probability of an impossible event is 1. (True / False)

  2. Probability of getting at least one head in two coin tosses is 3/4. (True / False)

Section B (6 Marks)

(Attempt any 3, 2 marks each)

  1. A die is thrown. Find the probability of getting an even number.

  2. A card is drawn from a deck. Find the probability of getting a king.

  3. Two coins are tossed. Find the probability of getting no head.

  4. A number is selected from 1 to 10. Find probability of getting a prime number.

  5. Find probability of selecting a leap year from first 5 consecutive years starting from 2016.

Section C (9 Marks)

(Attempt any 3, 3 marks each)

  1. Two dice are thrown. Find the probability that sum is 8.

  2. A card is drawn. Find probability of getting:
    (i) a spade
    (ii) a non-face card

  3. Two coins are tossed. Find probability of:
    (i) at least one head
    (ii) at most one head

  4. From numbers 1 to 20, one number is selected. Find probability of:
    (i) multiple of 3
    (ii) not a multiple of 3

  5. A die is thrown twice. Find probability of getting same number both times.

Section D (8 Marks)

(Attempt any 2, 4 marks each)

  1. Two dice are thrown simultaneously. Find probability of:
    (i) sum is greater than 9
    (ii) sum is at most 5

  2. A card is drawn from a pack. Find probability of:
    (i) a red face card
    (ii) a black card which is not a king

  3. A year is selected randomly from 2010 to 2020. Find probability that it is:
    (i) a leap year
    (ii) not a leap year


✅ ANSWER KEY WITH DETAILED SOLUTIONS & MARKING SCHEME

Section A (7 Marks)

Q1. MCQs (1 mark each)

1. Numbers greater than 4 → {5, 6} → 2 outcomes
Total outcomes = 6
Probability = 2/6 = 1/3
✔ Answer: (B) 1/3

2. Sample space: {HH, HT, TH, TT}
Exactly one head → {HT, TH} → 2 outcomes
Probability = 2/4 = 1/2
✔ Answer: (B) 1/2

3. Red cards = 26 out of 52
Probability = 26/52 = 1/2
✔ Answer: (B) 1/2

👉 Marking: 1 mark each (No step marking)

Q2. Fill in the blanks (1 mark each)

4. Probability of tail = 1/2
✔ Answer: 1/2

5. Numbers less than 7 → all outcomes (1–6)
Probability = 6/6 = 1
✔ Answer: 1

👉 Marking: Full 1 mark each (no partial)

Q3. True/False (1 mark each)

6. Impossible event probability = 0 ❌
✔ Answer: False

7. At least one head → 3/4 ✔
✔ Answer: True

👉 Marking: 1 mark each

Section B (6 Marks) (Attempt any 3)

👉 Marking scheme:

  • Formula / Approach = 1 mark

  • Final Answer = 1 mark

8. Even number on die → {2,4,6} → 3 outcomes
Probability = 3/6 = 1/2

9. Kings = 4 cards
Probability = 4/52 = 1/13

10. No head → {TT} → 1 outcome
Probability = 1/4

11. Prime numbers (1–10) → {2,3,5,7} → 4 outcomes
Probability = 4/10 = 2/5

12. Years: 2016,17,18,19,20 → Leap years: 2016, 2020 → 2
Probability = 2/5

Section C (9 Marks) (Attempt any 3)

👉 Marking scheme (3 marks):

  • Sample space / logic = 1 mark

  • Correct favorable outcomes = 1 mark

  • Final probability = 1 mark

13. Sum = 8 (two dice)
Possible pairs: (2,6),(3,5),(4,4),(5,3),(6,2) → 5
Total = 36
Probability = 5/36

14. Cards
(i) Spade = 13/52 = 1/4
(ii) Non-face cards = 52 – 12 = 40
Probability = 40/52 = 10/13

15. Coins
(i) At least one head = 3/4
(ii) At most one head → {TT, HT, TH} → 3/4

16. Numbers (1–20)
(i) Multiples of 3 → {3,6,9,12,15,18} → 6
Probability = 6/20 = 3/10
(ii) Not multiple = 14/20 = 7/10

17. Same number twice
Pairs: (1,1)…(6,6) → 6
Probability = 6/36 = 1/6

Section D (8 Marks) (Attempt any 2)

👉 Marking scheme (4 marks):

  • Total outcomes = 1 mark

  • Favorable outcomes (each part) = 1+1 mark

  • Final answer = 1 mark

18. Two dice
(i) Sum > 9 → sums: 10,11,12
Pairs = 3 + 2 + 1 = 6
Probability = 6/36 = 1/6

(ii) Sum ≤ 5 → sums: 2,3,4,5 → 1+2+3+4 = 10
Probability = 10/36 = 5/18

19. Cards
(i) Red face cards → 6
Probability = 6/52 = 3/26

(ii) Black not king → Black cards = 26, remove 2 kings → 24
Probability = 24/52 = 6/13

20. Years (2010–2020 → 11 years)
Leap years → 2012, 2016, 2020 → 3
(i) Probability = 3/11
(ii) Not leap = 8/11

📊 PAPER ANALYSIS (VERY IMPORTANT FOR TEACHER)

🔹 Difficulty Level

  • Section A: Easy (direct formula-based)

  • Section B: Easy–Moderate

  • Section C: Moderate (requires listing outcomes carefully)

  • Section D: Moderate (case-based thinking)

👉 Overall: Balanced & Board-Level Perfect Paper

🔹 Concept Coverage

✔ Coins (basic + at least/at most)
✔ Dice (single + double)
✔ Cards (face, color, suit)
✔ Leap year (real-life application)
✔ Number selection (prime, multiples)

👉 Matches NCERT + GSEB perfectly

🔹 Common Mistakes Students Will Make

❌ Forgetting total outcomes (36 in dice)
❌ Confusing “at least” vs “at most”
❌ Counting face cards wrongly (12 total)
❌ Leap year logic mistake (divisible by 4 rule)
❌ Not simplifying fractions

🎯 PRO TIPS FOR BOARD EXAMS (GSEB 10 Maths)

🔥 1. Always Write Sample Space

Even if not asked → gives extra clarity + marks safety

🔥 2. Learn Standard Results

  • Coin (2 toss) → 4 outcomes

  • Dice (2 dice) → 36 outcomes

  • Cards → 52 total

👉 Saves time in exam

🔥 3. Keywords Trick

  • “At least one” → use complement OR direct (exclude none)

  • “At most one” → includes 0 and 1

🔥 4. Presentation = Marks

Write like:
Total outcomes =
Favorable outcomes =
Probability =

👉 Examiner gives full marks easily

🔥 5. Avoid Calculation Mistakes

  • Simplify fractions properly

  • Don’t skip steps in 3 & 4 mark questions

🔥 6. Time Strategy

  • Section A → 5 min

  • Section B → 10 min

  • Section C → 15 min

  • Section D → 15 min

🔥 7. Practice Priority

Must practice:
✔ Two dice sums
✔ Cards (face/red/black)
✔ At least / At most


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