VEDANT WORKSHEET SERIES

Class: X
Subject: Mathematics
Chapter: 14 – Probability
Time: 1 Hour
Maximum Marks: 20

SECTION A – CASE STUDY QUESTIONS (5 × 4 = 20 Marks)

Q1.
A school conducts a game where a student throws a fair die. The number obtained determines the prize category. Numbers 1 and 2 correspond to small prizes, 3 and 4 to medium prizes, and 5 and 6 to big prizes. All outcomes are equally likely.

a) Find the probability of getting a small prize. (1)
b) Find the probability of getting a number greater than 4. (1)
c) Find the probability of getting either a medium or big prize. (2)

Q2.
Two fair coins are tossed simultaneously during a classroom activity. The possible outcomes are recorded and analyzed. The teacher asks students to observe patterns and probabilities based on outcomes.

a) Write the sample space. (1)
b) Find the probability of getting exactly one head. (1)
c) Find the probability of getting at least one tail. (2)

Q3.
A card is drawn at random from a well-shuffled deck of 52 playing cards. The deck contains 4 suits: hearts, diamonds, clubs, and spades. Each suit has 13 cards including face cards (J, Q, K).

a) Find the probability of getting a red card. (1)
b) Find the probability of getting a king. (1)
c) Find the probability of getting a non-face card. (2)

Q4.
A number is selected at random from the first 20 natural numbers. Students are asked to classify numbers as prime, composite, or special numbers based on their properties.

a) Find the probability of selecting a prime number. (1)
b) Find the probability of selecting a multiple of 3. (1)
c) Find the probability of selecting a number that is both even and a multiple of 5. (2)

Q5.
A calendar year is selected at random. The teacher discusses leap years and non-leap years and how the number of days varies. Based on this, students calculate probabilities related to days of the week.

a) Find the probability that a randomly selected year is a leap year (assuming 1 leap year in every 4 years). (1)
b) In a leap year, find the probability that there are 53 Sundays. (1)
c) In a non-leap year, find the probability that there are 53 Mondays. (2)

✅ VEDANT WORKSHEET SERIES – DETAILED SOLUTIONS

Class 10 – Chapter 14: Probability
Maximum Marks: 20

🔷 Q1. Die Based Case

Given:

A fair die → outcomes = {1,2,3,4,5,6}
Total outcomes (n(S)) = 6

(a) Probability of small prize

Small prize → numbers {1,2}
Favourable outcomes (n(E)) = 2

P(E) = n(E)/n(S) = 2/6 = 1/3

Marking Scheme:

Identifying outcomes = 0.5
Formula & answer = 0.5

(b) Number greater than 4

Numbers > 4 → {5,6}
n(E) = 2

P = 2/6 = 1/3

Marks:

Outcomes = 0.5
Answer = 0.5

(c) Medium or Big prize

Medium → {3,4}
Big → {5,6}
Combined → {3,4,5,6}

n(E) = 4

P = 4/6 = 2/3

Marks:

Correct cases = 1
Simplification = 1

🔷 Q2. Two Coins

(a) Sample Space

Two coins → each has H or T

S = {HH, HT, TH, TT}
n(S) = 4

Marks:

Listing = 1

(b) Exactly one head

Cases → HT, TH
n(E) = 2

P = 2/4 = 1/2

Marks:

Correct cases = 0.5
Answer = 0.5

(c) At least one tail

“At least one tail” means → 1 or more tails

Cases → HT, TH, TT
n(E) = 3

P = 3/4

Marks:

Interpretation = 1
Answer = 1

🔷 Q3. Playing Cards

Given:

Total cards = 52

(a) Red card

Red cards = hearts + diamonds = 26

P = 26/52 = 1/2

Marks: 1

(b) King

Kings = 4

P = 4/52 = 1/13

Marks: 1

(c) Non-face card

Face cards = J, Q, K → 3 per suit
Total face cards = 3 × 4 = 12

Non-face cards = 52 − 12 = 40

P = 40/52 = 10/13

Marks:

Finding non-face = 1
Final answer = 1

🔷 Q4. Numbers 1 to 20

Given:

Total numbers = 20

(a) Prime numbers

Prime numbers ≤ 20 →
2,3,5,7,11,13,17,19

Count = 8

P = 8/20 = 2/5

Marks: 1

(b) Multiples of 3

3,6,9,12,15,18 → 6 numbers

P = 6/20 = 3/10

Marks: 1

(c) Even and multiple of 5

Multiples of 5 → 5,10,15,20
Even numbers among them → 10,20

n(E) = 2

P = 2/20 = 1/10

Marks:

Selection logic = 1
Final answer = 1

🔷 Q5. Calendar Based

(a) Leap year probability

Given assumption:

P = 1/4

Marks: 1

(b) Leap year → 53 Sundays

Leap year days = 366

366 = 52 weeks + 2 extra days

Extra days can be:
(Sun, Mon), (Mon, Tue), … (Sat, Sun) → total 7 possibilities

To get 53 Sundays → Sunday must be in extra days

Favourable cases = 2

P = 2/7

Marks:

Concept = 0.5
Answer = 0.5

(c) Non-leap year → 53 Mondays

Non-leap days = 365

365 = 52 weeks + 1 extra day

Extra day can be any one of 7 days

To get 53 Mondays → extra day must be Monday

P = 1/7

Marks:

Concept = 1
Answer = 1

📊 Paper Analysis (Detailed)

✅ Level: Easy but Concept-Based

No tricky numericals
Strong focus on interpretation
Case study = real exam pattern

📌 Chapter Coverage:

✔ Classical probability
✔ Events & sample space
✔ Complementary cases
✔ Calendar problems ⭐
✔ Cards & coins

⚠️ Where Students Lose Marks:

Not writing sample space
Missing favourable cases
Wrong interpretation of “at least”
Calendar confusion

🎯 Board Exam Pro Strategy

🔥 1. Follow 3-Step Rule

Always write:

n(S) = Total outcomes  
n(E) = Favourable outcomes  
P = n(E)/n(S)

🔥 2. Write cases clearly (VERY IMPORTANT)

Even if answer is correct → no steps = less marks

🔥 3. Calendar Shortcut (Must Learn)

Leap year → 2/7  
Non-leap → 1/7

🔥 4. Learn standard counts

Situation	Outcomes
Die	6
2 coins	4
Cards	52
2 dice	36

🔥 5. Time Strategy

Each case study → 3–4 min
Total paper → finish in 40 min
Last 20 min → revision

⚠️ COMMON MISTAKES SHEET – PROBABILITY

🚫 1. Forgetting Total Outcomes (n(S))

❌ Mistake:

Student directly writes probability without writing total outcomes.

✅ Correct Approach:

Always write:


n(S) = total outcomes
n(E) = favourable outcomes
P = n(E)/n(S)

👉 Board gives step marks for this

🚫 2. Not Writing Sample Space (Coins/Dice)

❌ Mistake:

Writing answer directly for coin questions.

✅ Correct:


S = {HH, HT, TH, TT}

👉 Without sample space → marks may be cut

🚫 3. Confusion in “At least” & “At most”

❌ Mistake:

“At least one” → students take only 1 case
“At most one” → students forget 0 case

✅ Correct Understanding:

Keyword	Meaning
At least one	1 or more
At most one	0 or 1
Exactly one	only 1

👉 Example:
“At least one head” = HH, HT, TH

🚫 4. Double Counting Cases

❌ Mistake:

Repeating outcomes or missing some

✅ Tip:

List systematically:


(1,1), (1,2), (1,3)... (6,6)

👉 Use table method for 2 dice

🚫 5. Not Simplifying Answers

❌ Mistake:

Leaving answer as:


6/36

✅ Correct:


6/36 = 1/6

👉 Always give simplified fraction

🚫 6. Card Problems Confusion

❌ Mistakes:

Thinking face cards = 10, J, Q, K
Forgetting suits

✅ Correct Facts:

Concept	Value
Total cards	52
Red cards	26
Face cards	12 (J, Q, K only)
Kings	4

🚫 7. Prime Numbers Mistake

❌ Mistake:

Including 1 as prime

✅ Correct:

Prime starts from 2

👉 Example:
2,3,5,7,...

🚫 8. Calendar Questions Confusion

❌ Mistake:

Trying long calculations

✅ Shortcut:


Leap year → 2 extra days → P = 2/7  
Non-leap → 1 extra day → P = 1/7

👉 Must memorize!

🚫 9. “Both” vs “Either” Confusion

❌ Mistake:

Mixing union and intersection

✅ Correct:

Term	Meaning
Both	A ∩ B
Either	A ∪ B

👉 Formula:


n(A ∪ B) = n(A) + n(B) − n(A ∩ B)

🚫 10. Not Reading Question Properly

❌ Mistake:

Missing keywords like:

“not”
“at least”
“greater than”

✅ Tip:

👉 Underline keywords before solving

🚫 11. Skipping Steps in Case Study

❌ Mistake:

Direct answer writing

✅ Board Expectation:

✔ Write cases
✔ Write formula
✔ Then answer

🚫 12. Writing Decimal Instead of Fraction

❌ Mistake:


P = 0.5

✅ Correct:


P = 1/2

👉 Always write fraction form

🚫 13. Wrong Counting in Range Questions

❌ Mistake:

Counting incorrectly in 1–20, 1–50 etc.

✅ Tip:

👉 Write numbers clearly
👉 Don’t count mentally

🚫 14. Ignoring Complement Method

❌ Mistake:

Long method instead of shortcut

✅ Smart Trick:


P(at least one) = 1 − P(none)

👉 Saves time in exams

🚫 15. Poor Presentation

❌ Mistake:

Messy work, no steps

✅ Ideal Format:


n(S) = ...
n(E) = ...
P = n(E)/n(S)

👉 Clean steps = extra marks

🎯 TOP 5 GOLDEN RULES (MUST FOLLOW)

✅ Always write n(S), n(E), P formula
✅ Always list outcomes clearly
✅ Always simplify fraction
✅ Always read keywords carefully
✅ Always show steps (never direct answer)

🧠 FINAL EXAM TIP

👉 Probability is 100% scoring chapter
👉 Students lose marks only due to carelessness, not difficulty

Class 10 Maths Case Study Worksheet Chapter 14 Probability | Detailed Solutions & Marking Scheme

VEDANT WORKSHEET SERIES

✅ VEDANT WORKSHEET SERIES – DETAILED SOLUTIONS

🔷 Q1. Die Based Case

Given:

(a) Probability of small prize

(b) Number greater than 4

(c) Medium or Big prize

🔷 Q2. Two Coins

(a) Sample Space

(b) Exactly one head

(c) At least one tail

🔷 Q3. Playing Cards

Given:

(a) Red card

(b) King

(c) Non-face card

🔷 Q4. Numbers 1 to 20

Given:

(a) Prime numbers

(b) Multiples of 3

(c) Even and multiple of 5

🔷 Q5. Calendar Based

(a) Leap year probability

(b) Leap year → 53 Sundays

(c) Non-leap year → 53 Mondays

📊 Paper Analysis (Detailed)

✅ Level: Easy but Concept-Based

📌 Chapter Coverage:

⚠️ Where Students Lose Marks:

🎯 Board Exam Pro Strategy

🔥 1. Follow 3-Step Rule

🔥 2. Write cases clearly (VERY IMPORTANT)

🔥 3. Calendar Shortcut (Must Learn)

🔥 4. Learn standard counts

🔥 5. Time Strategy

⚠️ COMMON MISTAKES SHEET – PROBABILITY

🚫 1. Forgetting Total Outcomes (n(S))

❌ Mistake:

✅ Correct Approach:

🚫 2. Not Writing Sample Space (Coins/Dice)

❌ Mistake:

✅ Correct:

🚫 3. Confusion in “At least” & “At most”

❌ Mistake:

✅ Correct Understanding:

🚫 4. Double Counting Cases

❌ Mistake:

✅ Tip:

🚫 5. Not Simplifying Answers

❌ Mistake:

✅ Correct:

🚫 6. Card Problems Confusion

❌ Mistakes:

✅ Correct Facts:

🚫 7. Prime Numbers Mistake

❌ Mistake:

✅ Correct:

🚫 8. Calendar Questions Confusion

❌ Mistake:

✅ Shortcut:

🚫 9. “Both” vs “Either” Confusion

❌ Mistake:

✅ Correct:

🚫 10. Not Reading Question Properly

❌ Mistake:

✅ Tip:

🚫 11. Skipping Steps in Case Study

❌ Mistake:

✅ Board Expectation:

🚫 12. Writing Decimal Instead of Fraction

❌ Mistake:

✅ Correct:

🚫 13. Wrong Counting in Range Questions

❌ Mistake:

✅ Tip:

🚫 14. Ignoring Complement Method

❌ Mistake:

✅ Smart Trick:

🚫 15. Poor Presentation