Class 10 Maths MCQ Worksheet Chapter 14 Probabiity | Detailed Solutions & Marking Scheme
VEDANT WORKSHEET SERIES
Class: X
Subject: Mathematics
Chapter: 14 – Probability
Time: 1 Hour
Maximum Marks: 30
SECTION A
Q1–Q15: Multiple Choice Questions (1 mark each)
Q1. A die is thrown once. What is the probability of getting a multiple of 2?
A. 1/6
B. 1/3
C. 1/2
D. 2/3
Q2. 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
Q3. A card is drawn from a well-shuffled deck. What is the probability of getting a queen?
A. 1/13
B. 1/4
C. 1/52
D. 4/13
Q4. A number is selected at random from 1 to 20. What is the probability that it is a prime number?
A. 4/20
B. 8/20
C. 9/20
D. 10/20
Q5. A die is thrown. What is the probability of getting a number less than 5?
A. 1/6
B. 2/3
C. 1/2
D. 5/6
Q6. Two dice are thrown. What is the probability that the sum is 7?
A. 1/6
B. 1/12
C. 1/36
D. 6/36
Q7. From numbers 1 to 30, one number is chosen at random. What is the probability that it is a multiple of 5?
A. 1/5
B. 2/5
C. 1/6
D. 1/3
Q8. A card is drawn. What is the probability of getting a red card?
A. 1/4
B. 1/2
C. 3/4
D. 1/13
Q9. A leap year is selected at random. What is the probability that it has 53 Sundays?
A. 1/7
B. 2/7
C. 3/7
D. 4/7
Q10. Three coins are tossed. What is the probability of getting exactly two heads?
A. 3/8
B. 1/8
C. 1/2
D. 5/8
Q11. A number from 1 to 50 is selected. What is the probability that it is a perfect square?
A. 5/50
B. 7/50
C. 6/50
D. 4/50
Q12. A die is thrown. What is the probability of getting a number which is both even and prime?
A. 1/6
B. 2/6
C. 3/6
D. 0
Q13. Two dice are thrown. What is the probability that the product is even?
A. 1/4
B. 3/4
C. 1/2
D. 2/3
Q14. A card is drawn. What is the probability that it is neither a king nor a queen?
A. 44/52
B. 48/52
C. 40/52
D. 45/52
Q15. A number from 1 to 100 is selected. What is the probability that it is divisible by both 2 and 5?
A. 1/10
B. 1/5
C. 1/20
D. 1/2
Q16–Q30: Assertion–Reason Questions (1 mark each)
For all questions, choose the correct option:
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
Q16.
Assertion (A): Probability of an impossible event is 0.
Reason (R): Total number of outcomes is always zero.
Q17.
Assertion (A): Probability of a sure event is 1.
Reason (R): All outcomes are favourable.
Q18.
Assertion (A): Probability lies between 0 and 1.
Reason (R): It is defined as favourable outcomes divided by total outcomes.
Q19.
Assertion (A): When a die is thrown, probability of getting 7 is 0.
Reason (R): 7 is not a possible outcome.
Q20.
Assertion (A): Probability of getting head when tossing a coin is 1/2.
Reason (R): There are two equally likely outcomes.
Q21.
Assertion (A): Probability of getting a red card is 1/2.
Reason (R): Half of the cards are red.
Q22.
Assertion (A): In a leap year, probability of 53 Sundays is 2/7.
Reason (R): Leap year has 366 days.
Q23.
Assertion (A): Probability of getting sum 12 with two dice is 1/36.
Reason (R): Only one outcome (6,6) gives sum 12.
Q24.
Assertion (A): Probability of getting a prime number on a die is 1/2.
Reason (R): Prime numbers on a die are 2, 3, 5.
Q25.
Assertion (A): Probability of selecting a vowel from English alphabets is 5/26.
Reason (R): There are 5 vowels in English alphabet.
Q26.
Assertion (A): Probability of getting at least one tail in two coin tosses is 3/4.
Reason (R): Only one outcome has no tail.
Q27.
Assertion (A): Probability of selecting a multiple of 3 from 1 to 9 is 1/3.
Reason (R): Multiples of 3 are 3, 6, 9.
Q28.
Assertion (A): Probability of getting an even number on a die is 1/2.
Reason (R): Even numbers are 2, 4, 6.
Q29.
Assertion (A): Probability of drawing a black card is 26/52.
Reason (R): There are two black suits.
Q30.
Assertion (A): Probability of selecting a factor of 12 from numbers 1 to 12 is 6/12.
Reason (R): Factors of 12 are 1, 2, 3, 4, 6, 12.
ANSWER KEY – VEDANT WORKSHEET SERIES (Probability)
SECTION A – MCQs (1 mark each)
Q1. Multiples of 2 on die = {2, 4, 6} → 3 outcomes
Probability = 3/6 = 1/2
Ans: C
Q2. Outcomes = {HH, HT, TH, TT}
At least one head = {HH, HT, TH} → 3
Probability = 3/4
Ans: C
Q3. Total cards = 52, Queens = 4
Probability = 4/52 = 1/13
Ans: A
Q4. Prime numbers (1–20) = 2,3,5,7,11,13,17,19 → 8
Probability = 8/20
Ans: B
Q5. Numbers < 5 = {1,2,3,4} → 4
Probability = 4/6 = 2/3
Ans: B
Q6. Sum 7 pairs = (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6
Total outcomes = 36
Probability = 6/36 = 1/6
Ans: A
Q7. Multiples of 5 (1–30) = 5,10,15,20,25,30 → 6
Probability = 6/30 = 1/5
Ans: A
Q8. Red cards = 26
Probability = 26/52 = 1/2
Ans: B
Q9. Leap year → 366 days = 52 weeks + 2 days
Extra days can be any 2 consecutive days
Favourable (53 Sundays) = Sunday + one more → 2 cases
Probability = 2/7
Ans: B
Q10. Outcomes (3 coins) = 8
Exactly 2 heads = {HHT, HTH, THH} → 3
Probability = 3/8
Ans: A
Q11. Perfect squares ≤ 50 = 1,4,9,16,25,36,49 → 7
Probability = 7/50
Ans: B
Q12. Even primes = {2}
Probability = 1/6
Ans: A
Q13. Product is even if at least one die shows even
Odd × odd gives odd → (3×3)=9 odd outcomes
Total = 36 → Even outcomes = 36 – 9 = 27
Probability = 27/36 = 3/4
Ans: B
Q14. Kings + Queens = 8
Remaining = 52 – 8 = 44
Probability = 44/52
Ans: A
Q15. Divisible by 2 and 5 → divisible by 10
Numbers = 10,20,…,100 → 10 numbers
Probability = 10/100 = 1/10
Ans: A
SECTION A – Assertion–Reason (1 mark each)
Q16. Impossible event = 0 ✔, Reason incorrect
Ans: C
Q17. Sure event = 1 ✔, All outcomes favourable ✔ (correct explanation)
Ans: A
Q18. Range 0 to 1 ✔, Definition correct ✔
Ans: A
Q19. 7 not possible ✔, explanation correct ✔
Ans: A
Q20. P(head)=1/2 ✔, two outcomes ✔ (correct explanation)
Ans: A
Q21. Red cards = 1/2 ✔, half cards red ✔
Ans: A
Q22. 53 Sundays = 2/7 ✔, leap year has 366 days ✔ but not full explanation
Ans: B
Q23. Sum 12 = 1/36 ✔, only (6,6) ✔
Ans: A
Q24. Prime outcomes = 3 → 3/6 = 1/2 ✔
Reason correct ✔
Ans: A
Q25. Vowels = 5 → probability = 5/26 ✔
Reason correct ✔
Ans: A
Q26. At least one tail = 3/4 ✔
Only one outcome (HH) has no tail ✔
Ans: A
Q27. Multiples of 3 = 3,6,9 → 3/9 = 1/3 ✔
Reason correct ✔
Ans: A
Q28. Even numbers = 3 → 3/6 = 1/2 ✔
Reason correct ✔
Ans: A
Q29. Black cards = 26 ✔
Two suits ✔ but not full explanation
Ans: B
Q30. Factors of 12 = 6 numbers ✔
Probability = 6/12 ✔
Reason correct ✔
Ans: A
MARKING SCHEME
• Each correct answer = 1 mark
• No negative marking
• Total Questions = 30
Total Marks = 30
Comments
Post a Comment