Class 10 Maths QP Worksheet Chapter 14 Probabilty | Detailed Solutions & Marking Scheme

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VEDANT WORKSHEET SERIES - ACADEMIC YEAR 2026-27

Class: 10
Subject: Mathematics
Chapter: 14 – Probability
Time: 1 Hour
Maximum Marks: 30

Section A (1 × 7 = 7 Marks)

Q1. A die is thrown once. What is the probability of getting a prime number?
A. 1/2
B. 1/3
C. 2/3
D. 1/6

Q2. A card is drawn from a well-shuffled deck of 52 playing cards. What is the probability of getting a red card?
A. 1/4
B. 1/2
C. 3/4
D. 13/52

Q3. Two coins are tossed simultaneously. What is the probability of getting at least one head?
A. 1/4
B. 1/2
C. 3/4
D. 1

Q4. A number is selected from 1 to 20. What is the probability that it is a multiple of 3?
A. 1/5
B. 1/4
C. 3/10
D. 7/20

Q5. What is the probability of getting a leap year when a year is selected at random from 2016 to 2023?
A. 1/4
B. 1/8
C. 1/2
D. 2/8

Q6. Assertion (A): The probability of an impossible event is 0.
Reason (R): The probability of an event lies between 0 and 1 (inclusive).
A. Both A and R are true, R is correct explanation of A
B. Both A and R are true, R is not correct explanation of A
C. A is true, R is false
D. A is false, R is true

Q7. Assertion (A): When two dice are thrown, the probability of getting sum 7 is 1/6.
Reason (R): There are 6 favourable outcomes for sum 7.
A. Both A and R are true, R is correct explanation of A
B. Both A and R are true, R is not correct explanation of A
C. A is true, R is false
D. A is false, R is true

Section B (2 × 4 = 8 Marks)

Q8. A card is drawn from a pack of 52 cards. Find the probability that the card drawn is:
(a) a king
(b) a non-face card

Q9. Find the probability of getting a number divisible by 4 when a number is selected at random from 1 to 40.

Q10. Two dice are thrown simultaneously. Find the probability of getting:
(a) a doublet
(b) sum less than 4

Q11. A letter is chosen at random from the word “PROBABILITY”. Find the probability that it is:
(a) a vowel
(b) a consonant

Section C (3 × 2 = 6 Marks)

Q12. A number is selected at random from first 50 natural numbers. Find the probability that the number is:
(a) a perfect square
(b) a multiple of both 2 and 5

Q13. Three coins are tossed simultaneously. Find the probability of getting:
(a) exactly two heads
(b) at most one tail

Section D (5 × 1 = 5 Marks)

Q14. A bag contains 5 red, 7 blue and 8 green balls. One ball is drawn at random.
(a) Find the probability that the ball drawn is not green.
(b) Find the probability that the ball drawn is either red or blue.
(c) If one more red ball is added, how does the probability of drawing a red ball change? Calculate the new probability.
(d) Is the event “getting a green ball” equally likely as “getting a blue ball”? Justify.

Section E (Case Study) (1 + 1 + 2 = 4 Marks)

Q15. Case Study: Student Attendance Analysis
In a class of 30 students, 12 students like Mathematics, 10 like Science, and 8 like both subjects.

Based on this information, answer the following:

(a) What is the probability that a randomly selected student likes Mathematics?

(b) What is the probability that a student likes both Mathematics and Science?

(c) Find the probability that a student likes at least one of the two subjects.

Here is your complete step-by-step solution with marking scheme, analysis, and board exam tips in easy-to-copy format 👇

✅ VEDANT WORKSHEET SERIES – SOLUTIONS

Class 10 – Chapter 14: Probability
Marks: 30

🔷 Section A (1 Mark Each)

Q1

Prime numbers on die = {2, 3, 5} → 3 outcomes
Total outcomes = 6

Probability = 3/6 = 1/2
✅ Answer: A

Marks: 1

Q2

Red cards = 26
Total = 52

Probability = 26/52 = 1/2
✅ Answer: B

Marks: 1

Q3

Sample space = {HH, HT, TH, TT} = 4
At least one head = {HH, HT, TH} = 3

Probability = 3/4
✅ Answer: C

Marks: 1

Q4

Multiples of 3 (1–20) = 3,6,9,12,15,18 → 6 numbers
Total = 20

Probability = 6/20 = 3/10
✅ Answer: C

Marks: 1

Q5

Years = 2016–2023 → total = 8
Leap years = 2016, 2020 → 2

Probability = 2/8 = 1/4
✅ Answer: A

Marks: 1

Q6

A: True (impossible event → 0)
R: True but does NOT explain A

✅ Answer: B

Marks: 1

Q7

Total outcomes (2 dice) = 36
Sum = 7 → favourable = 6

Probability = 6/36 = 1/6

A: True
R: True and explains A

✅ Answer: A

Marks: 1

🔷 Section B (2 Marks Each)

Q8

Total cards = 52

(a) Kings = 4
P = 4/52 = 1/13

(b) Face cards = 12 → non-face = 40
P = 40/52 = 10/13

Marks:

  • Each part = 1 mark

Q9

Multiples of 4 (1–40) = 4,8,...,40 → 10 numbers

Probability = 10/40 = 1/4

Marks:

  • Favourable = 1 mark

  • Final answer = 1 mark

Q10

Total outcomes = 36

(a) Doublet = (1,1),(2,2)...(6,6) → 6
P = 6/36 = 1/6

(b) Sum < 4 → (1,1),(1,2),(2,1) → 3
P = 3/36 = 1/12

Marks:

  • Each part = 1 mark

Q11

Word = PROBABILITY → total letters = 11

(a) Vowels = O,A,I,I → 4
P = 4/11

(b) Consonants = 7
P = 7/11

Marks:

  • Each part = 1 mark

🔷 Section C (3 Marks Each)

Q12

Total numbers = 50

(a) Perfect squares ≤ 50 → 1,4,9,16,25,36,49 → 7
P = 7/50

(b) Multiple of 2 & 5 → LCM = 10
Numbers = 10,20,30,40,50 → 5
P = 5/50 = 1/10

Marks:

  • Each part: 1.5 marks

Q13

Sample space (3 coins) = 8

(a) Exactly 2 heads → HHT, HTH, THH → 3
P = 3/8

(b) At most 1 tail → HHH, HHT, HTH, THH → 4
P = 4/8 = 1/2

Marks:

  • Each part: 1.5 marks

🔷 Section D (5 Marks)

Total balls = 5 + 7 + 8 = 20

(a) Not green

= red + blue = 5 + 7 = 12
P = 12/20 = 3/5

Marks: 1

(b) Red or blue

Same as above

P = 12/20 = 3/5

Marks: 1

(c) After adding 1 red ball

New total = 21
Red = 6

New P = 6/21 = 2/7

Marks: 2

  • Setup = 1

  • Answer = 1

(d) Compare green & blue

Green = 8/20
Blue = 7/20

Not equal → Not equally likely

Marks: 1

🔷 Section E (Case Study)

Total students = 30

Maths = 12
Science = 10
Both = 8

(a) Likes Maths

P = 12/30 = 2/5

Marks: 1

(b) Likes both

P = 8/30 = 4/15

Marks: 1

(c) At least one

Formula:
n(A ∪ B) = n(A) + n(B) − n(A ∩ B)

= 12 + 10 − 8 = 14

P = 14/30 = 7/15

Marks: 2

📊 Paper Analysis

✅ Difficulty Level: Easy to Moderate

  • Section A: Very easy (direct formula-based)

  • Section B: Basic application

  • Section C: Slightly conceptual

  • Section D: Standard board-level case

  • Section E: Important concept (union formula)

📌 Important Topics Covered:

  • Classical probability

  • Dice & coins

  • Cards

  • Counting method

  • “At least / at most”

  • Union formula (VERY IMPORTANT)

🎯 Pro Tips for Board Exam

🔥 1. Always write formula

Example:

Probability = Favourable outcomes / Total outcomes

👉 Gives step marks even if answer is wrong

🔥 2. Memorize standard results

  • 1 die → 6 outcomes

  • 2 dice → 36 outcomes

  • 3 coins → 8 outcomes

🔥 3. Focus on keywords

  • “At least one” → subtract from total

  • “At most” → include smaller cases

  • “Both” → intersection

🔥 4. Avoid common mistakes

❌ Forgetting total outcomes
❌ Not simplifying fractions
❌ Counting wrong cases

🧠 Final Strategy

👉 Attempt Section A in 5 minutes
👉 Section B + C in 25 minutes
👉 Leave 10 minutes for Section D & E carefully


 

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