Q1. In a single throw of a fair die, what is the probability of getting a number greater than 4?
(a) 1/6
(b) 1/3
(c) 1/2
(d) 2/3
Answer: (b)
Explanation: The favourable outcomes are 5 and 6 → 2 outcomes. Total outcomes = 6. Probability = 2/6 = 1/3.
Q2. A bag contains 5 red, 3 green and 2 blue balls. If one ball is drawn at random, what is the probability that it is not green? (a) 3/10
(b) 7/10
(c) 2/5
(d) 1/2
Answer: (b) Explanation: Total balls = 10. Non‑green balls = 5 red + 2 blue = 7. Probability = 7/10.
Q3. Two coins are tossed simultaneously. What is the probability of getting exactly one head?
(a) 1/4
(b) 1/2
(c) 3/4 (d) 1
Answer: (b)
Explanation: Sample space = {HH, HT, TH, TT}. Favourable = {HT, TH} → 2 outcomes. Probability = 2/4 = 1/2.
Q4. From a deck of 52 cards, one card is drawn at random. The probability that the card is a king or a queen is:
(a) 1/13
(b) 2/13
(c) 4/13
(d) 8/52 Answer: (b)
Explanation: There are 4 kings and 4 queens = 8 favourable cards. Probability = 8/52 = 2/13.
Q5. If the probability of an event occurring is 0.35, what is the probability that it does not occur?
(a) 0.35 (b) 0.65
(c) 0.5
(d) 0.25
Answer: (b)
Explanation: P(not A) = 1 – P(A) = 1 – 0.35 = 0.65.
Q6. In a class of 30 students, 18 play cricket, 12 play football and 5 play both. What is the probability that a randomly selected student plays either cricket or football? (a) 0.5
(b) 0.6
(c) 0.833
(d) 0.9
Answer: (c)
Explanation: Using addition rule: P(C∪F) = P(C)+P(F)−P(C∩F) = 18/30 + 12/30 − 5/30 = 25/30 = 5/6 ≈ 0.833.
Q7. A box contains 4 defective and 6 non‑defective bulbs. Two bulbs are drawn at random without replacement. What is the probability that both are defective?
(a) 2/15
(b) 1/15
(c) 4/25 (d) 6/25
Answer: (b)
Explanation: P(first defective)=4/10. After removing one defective, 3 defective left out of 9. P(second defective)=3/9=1/3. Combined = (4/10)(1/3)=4/30=2/15? Wait recalc: 4/10 3/9 = 12/90 = 2/15. Actually answer should be 2/15 (option a). Let’s correct: The correct answer is 2/15. So adjust options: we had a) 2/15, b)1/15 etc. Answer a). Explanation accordingly.
Q8. A die is rolled twice. What is the probability that the sum of the numbers on the two faces is 7?
(a) 1/6 (b) 1/12
(c) 1/36
(d) 5/36
Answer: (a)
Explanation: Favourable pairs: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6 outcomes. Total outcomes = 6×6=36. Probability = 6/36 = 1/6.
Q9. In a lottery, there are 10 tickets and only 1 winning ticket. If a person buys 2 tickets, what is the probability of winning at least one prize?
(a) 1/5
(b) 3/10
(c) 19/45
(d) 2/9
Answer: (c)
Explanation: Probability of no win = (9/10)*(8/9)=8/10=4/5. So probability of at least one win = 1‑4/5 = 1/5? Wait compute correctly: Without replacement: first ticket lose prob=9/10, second lose prob=8/9 → product=72/90=4/5. So win at least one = 1‑4/5=1/5. That’s option a. Let’s adjust options: make a) 1/5 correct. Provide explanation.
Q10. A bag contains 7 white and 5 black balls. Two balls are drawn at random with replacement. What is the probability that both are black?
(a) 25/144
(b) 5/12
(c) 25/144? Actually compute: P(black)=5/12. With replacement, both black = (5/12)^2 = 25/144. So answer a).
Q11. The odds in favour of an event are 3:2. What is the probability of the event?
(a) 3/5 (b) 2/5
(c) 3/2
(d) 5/3
Answer: (a)
Explanation: Odds in favour = p/(1-p) = 3/2 → p = 3/(3+2)=3/5.
Q12. If P(A)=0.4, P(B)=0.5 and P(A∩B)=0.2, then P(A∪B) is:
(a) 0.7 (b) 0.9
(c) 0.3
(d) 0.1
Answer: (a)
Explanation: P(A∪B)=P(A)+P(B)−P(A∩B)=0.4+0.5−0.2=0.7.
Q13. A fair coin is tossed three times. What is the probability of getting at least two heads?
(a) 1/2
(b) 3/8
(c) 1/4
(d) 1/8
Answer: (a)
Explanation: Total outcomes=8. Favourable: HHT, HTH, THH, HHH → 4 outcomes. Probability=4/8=1/2.
Q14. From a group of 8 men and 6 women, a committee of 3 is to be formed. What is the probability that the committee consists of exactly 2 women? (a) 15/91 (b) 30/91 (c) 45/91 (d) 60/91 Answer: (b)
Explanation: Ways to choose 2 women from 6 = C(6,2)=15; choose 1 man from 8 = C(8,1)=8 → favourable =15×8=120. Total ways = C(14,3)=364. Probability=120/364=30/91 after simplification.
Q15. The probability that it will rain on a given day is 0.3. What is the probability that it will not rain on two consecutive days?
(a) 0.09
(b) 0.21 (c) 0.49
(d) 0.7
Answer: (c)
Explanation: P(no rain)=1‑0.3=0.7. For two independent days: 0.7×0.7=0.49.
Q16. In a single throw of two dice, what is the probability of getting a doublet (same number on both dice)? (a) 1/6
(b) 1/12
(c) 1/36
(d) 1/3
Answer: (a)
Explanation: Doublets: (1,1),(2,2),(3,3),(4,4),(5,5),(6,6) → 6 outcomes. Total outcomes=36 → probability=6/36=1/6.
Q17. A box contains 3 red, 4 blue and 5 green balls. If two balls are drawn at random without replacement, what is the probability that one is red and the other is blue?
(a) 12/55
(b) 6/55
(c) 24/55
(d) 8/55
Answer: (a)
Explanation: Ways: red then blue = 3/12 4/11 =12/132; blue then red = 4/12 3/11 =12/132. Sum =24/132=2/11=12/55 after simplification? Let’s compute: 24/132 = divide by 12 → 2/11. 2/11 = multiply numerator and denominator by5 →10/55. Hmm mismatch. Let’s recalc properly: Total balls=12. Number of ways to pick 2 balls = C(12,2)=66. Favourable ways: choose 1 red from 3 (C3,1=3) and 1 blue from 4 (C4,1=4) → 34=12. Probability=12/66=2/11≈0.1818. Convert to denominator 55: 2/11 = (25)/(11*5)=10/55. So correct answer should be 10/55, not given. Adjust options: make option (a) 10/55. Provide explanation.
Q18. If the probability of an event A is 0.8, what is the probability of the complement of A?
(a) 0.2
(b) 0.8
(c) 0.5
(d) 1.8
Answer: (a)
Explanation: P(A’) = 1 – P(A) = 1 – 0.8 = 0.2.
Q19. A card is drawn from a well‑shuffled pack of 52 cards. Find the probability that the card is a face card (Jack, Queen, King).
(a) 3/13
(b) 1/13
(c) 12/52
(d) 1/4
Answer: (a)
Explanation: There are 3 face cards per suit × 4 suits = 12 face cards. Probability = 12/52 = 3/13.
Q20. Three unbiased coins are tossed. What is the probability of getting at most one head?
(a) 1/2
(b) 1/4
(c) 3/8
(d) 1/8
Answer: (c)
Explanation: Outcomes with 0 heads: TTT (1). Outcomes with exactly 1 head: HTT, THT, TTH (3). Total favourable =4. Probability =4/8=1/2? Wait that’s 0.5. Actually at most one head includes 0 or 1 head → 4 outcomes → probability=4/8=1/2. So answer should be 1/2 (option a). Let’s adjust: make option a) 1/2 correct.
Q21. In a class, 40% of students study Mathematics, 30% study Physics and 15% study both. What is the probability that a randomly selected student studies either Mathematics or Physics?
(a) 0.55
(b) 0.65
(c) 0.75
(d) 0.85 Answer: (a)
Explanation: Using inclusion‑exclusion: P(M∪P)=0.40+0.30−0.15=0.55.
Q22. A die is rolled. What is the probability of getting an even number or a number greater than 4? (a) 1/2
(b) 2/3
(c) 5/6
(d) 1
Answer: (b)
Explanation: Even numbers = {2,4,6}. Numbers >4 = {5,6}. Union = {2,4,5,6} → 4 outcomes. Probability = 4/6 = 2/3.
Q23. From a bag containing 5 red and 7 black balls, two balls are drawn at random without replacement. What is the probability that both balls are of the same colour?
(a) 31/66
(b) 35/66
(c) 5/12
(d) 1/2
Answer: (a)
Explanation: Ways to get both red = C(5,2)=10. Both black = C(7,2)=21. Favourable =31. Total ways = C(12,2)=66. Probability =31/66.
Q24. If two events A and B are mutually exclusive, then P(A∩B) equals:
(a) P(A)+P(B)
(b) 0
(c) P(A)·P(B)
(d) 1 Answer: (b)
Explanation: Mutually exclusive events cannot occur together, so their intersection is empty → probability 0.
Q25. A box contains 8 defective and 12 non‑defective bulbs. If three bulbs are selected at random with replacement, what is the probability that exactly one of them is defective?
(a) 96/125
(b) 48/125
(c) 12/125
(d) 36/125
Answer: (b)
Explanation: P(defective)=8/20=2/5, P(good)=3/5. For exactly one defective in three trials: C(3,1)(2/5)(3/5)^2 = 3(2/5)(9/25)=54/125? Wait compute: (2/5)(9/25)=18/125; times 3 =54/125. That’s not an option. Let’s adjust numbers: maybe use 6 defective, 14 good? Let’s craft a simpler: Box contains 4 defective and 6 good. P(def)=0.4, P(good)=0.6. Exactly one defective in 3 draws with replacement: C(3,1)0.40.6^2 =30.40.36=0.432 =432/1000=108/250=54/125. Still not nice. Choose numbers that give a simple fraction: Let defective=1, good=4 → P(def)=1/5, P(good)=4/5. Exactly one defective: 3(1/5)(4/5)^2 =3(1/5)*(16/25)=48/125. That’s option b. So adjust scenario: box contains 1 defective and 4 non‑defective bulbs. Then answer 48/125. Provide explanation.
Now compile all Qs with proper formatting. Ensure each Q is numbered, options labelled (a)-(d), answer line, explanationQ1. In a single throw of a fair die, what is the probability of getting a number greater than 4?
(a) 1/6
(b) 1/3
(c) 1/2
(d) 2/3
Answer: (b)
Explanation: The favourable outcomes are 5 and 6 → 2 outcomes. Total outcomes = 6. Probability = 2/6 = 1/3.
Q2. A bag contains 5 red, 3 green and 2 blue balls. If one ball is drawn at random, what is the probability that it is not green?
(a) 3/10
(b) 7/10
(c) 2/5
(d) 1/2
Answer: (b)
Explanation: Total balls = 10. Non‑green balls = 5 red + 2 blue = 7. Probability = 7/10.
Q3. Two coins are tossed simultaneously. What is the probability of getting exactly one head?
(a) 1/4
(b) 1/2
(c) 3/4
(d) 1
Answer: (b)
Explanation: Sample space = {HH, HT, TH, TT}. Favourable = {HT, TH} → 2 outcomes. Probability = 2/4 = 1/2.
Q4. From a deck of 52 cards, one card is drawn at random. The probability that the card is a king or a queen is:
(a) 1/13
(b) 2/13
(c) 4/13
(d) 8/52
Answer: (b) Explanation: There are 4 kings and 4 queens = 8 favourable cards. Probability = 8/52 = 2/13.
Q5. If the probability of an event occurring is 0.35, what is the probability that it does not occur?
(a) 0.35
(b) 0.65
(c) 0.5
(d) 0.25 Answer: (b)
Explanation: P(not A) = 1 – P(A) = 1 – 0.35 = 0.65.
Q6. In a class of 30 students, 18 play cricket, 12 play football and 5 play both. What is the probability that a randomly selected student plays either cricket or football?
(a) 0.5
(b) 0.6
(c) 0.833
(d) 0.9
Answer: (c)
Explanation: Using addition rule: P(C∪F) = P(C)+P(F)−P(C∩F) = 18/30 + 12/30 − 5/30 = 25/30 = 5/6 ≈ 0.833.
Q7. A box contains 4 defective and 6 non‑defective bulbs. Two bulbs are drawn at random without replacement. What is the probability that both are defective?
(a) 2/15
(b) 1/15
(c) 4/25 (d) 6/25
Answer: (a)
Explanation: P(first defective)=4/10. After removing one defective, 3 defective left out of 9. P(second defective)=3/9=1/3. Combined = (4/10)*(1/3)=4/30=2/15.
Q8. A die is rolled twice. What is the probability that the sum of the numbers on the two faces is 7?
(a) 1/6
(b) 1/12
(c) 1/36
(d) 5/36 Answer: (a)
Explanation: Favourable pairs: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) → 6 outcomes. Total outcomes = 6×6=36. Probability = 6/36 = 1/6.
Q9. In a lottery, there are 10 tickets and only 1 winning ticket. If a person buys 2 tickets, what is the probability of winning at least one prize?
(a) 1/5
(b) 3/10
(c) 19/45
(d) 2/9
Answer: (a)
Explanation: Probability of no win = (9/10)*(8/9)=8/10=4/5. So probability of at least one win = 1‑4/5 = 1/5.
Q10. A bag contains 7 white and 5 black balls. Two balls are drawn at random with replacement. What is the probability that both are black?
(a) 25/144
(b) 5/12
(c) 35/144
(d) 1/4
Answer: (a)
Explanation: P(black)=5/12. With replacement, both black = (5/12)^2 = 25/144.
Q11. The odds in favour of an event are 3:2. What is the probability of the event?
(a) 3/5
(b) 2/5 (c) 3/2
(d) 5/3
Answer: (a)
Explanation: Odds in favour = p/(1-p) = 3/2 → p = 3/(3+2)=3/5.
Q12. If P(A)=0.4, P(B)=0.5 and P(A∩B)=0.2, then P(A∪B) is:
(a) 0.7
(b) 0.9
(c) 0.3
(d) 0.1
Answer: (a)
Explanation: P(A∪B)=P(A)+P(B)−P(A∩B)=0.4+0.5−0.2=0.7.
Q13. A fair coin is tossed three times. What is the probability of getting at least two heads?
(a) 1/2
(b) 3/8
(c) 1/4
(d) 1/8
Answer: (a)
Explanation: Total outcomes=8. Favourable: HHT, HTH, THH, HHH → 4 outcomes. Probability=4/8=1/2.
Q14. From a group of 8 men and 6 women, a committee of 3 is to be formed. What is the probability that the committee consists of exactly 2 women?
(a) 15/91
(b) 30/91
(c) 45/91
(d) 60/91
Answer: (b)
Explanation: Ways to choose 2 women from 6 = C(6,2)=15; choose 1 man from 8 = C(8,1)=8 → favourable =15×8=120. Total ways = C(14,3)=364. Probability=120/364=30/91 after simplification.
Q15. The probability that it will rain on a given day is 0.3. What is the probability that it will not rain on two consecutive days?
(a) 0.09 (b) 0.21
(c) 0.49
(d) 0.7
Answer: (c)
Explanation: P(no rain)=1‑0.3=0.7. For two independent days: 0.7×0.7=0.49.
Q16. In a single throw of two dice, what is the probability of getting a doublet (same number on both dice)?
(a) 1/6
(b) 1/12
(c) 1/36
(d) 1/3
Answer: (a) Explanation: Doublets: (1,1),(2,2),(3,3),(4,4),(5,5),(6,6) → 6 outcomes. Total outcomes=36 → probability=6/36=1/6.
Q17. A box contains 3 red, 4 blue and 5 green balls. If two balls are drawn at random without replacement, what is the probability that one is red and the other is blue? (a) 10/55 (b) 6/55
(c) 24/55
(d) 8/55
Answer: (a)
Explanation: Total ways to pick 2 balls = C(12,2)=66. Favourable ways: choose 1 red from 3 (C3,1=3) and 1 blue from 4 (C4,1=4) → 3×4=12. Probability =12/66=2/11=10/55.
Q18. If the probability of an event A is 0.8, what is the probability of the complement of A?
(a) 0.2
(b) 0.8
(c) 0.5 (d) 1.8
Answer: (a)
Explanation: P(A’) = 1 – P(A) = 1 – 0.8 = 0.2.
Q19. A card is drawn from a well‑shuffled pack of 52 cards. Find the probability that the card is a face card (Jack, Queen, King).
(a) 3/13
(b) 1/13
(c) 12/52
(d) 1/4
Answer: (a)
Explanation: There are 3 face cards per suit × 4 suits = 12 face cards. Probability = 12/52 = 3/13.
Q20. Three unbiased coins are tossed. What is the probability of getting at most one head?
(a) 1/2
(b) 1/4
(c) 3/8
(d) 1/8
Answer: (a)
Explanation: Outcomes with 0 heads: TTT (1). Outcomes with exactly 1 head: HTT, THT, TTH (3). Total favourable =4. Probability =4/8=1/2.
Q21. In a class, 40% of students study Mathematics, 30% study Physics and 15% study both. What is the probability that a randomly selected student studies either Mathematics or Physics?
(a) 0.55
(b) 0.65 (c) 0.75
(d) 0.85
Answer: (a)
Explanation: Using inclusion‑exclusion: P(M∪P)=0.40+0.30−0.15=0.55.
Q22. A die is rolled. What is the probability of getting an even number or a number greater than 4?
(a) 1/2
(b) 2/3
(c) 5/6
(d) 1
Answer: (b)
Explanation: Even numbers = {2,4,6}. Numbers >4 = {5,6}. Union = {2,4,5,6} → 4 outcomes. Probability = 4/6 = 2/3.
Q23. From a bag containing 5 red and 7 black balls, two balls are drawn at random without replacement. What is the probability that both balls are of the same colour?
(a) 31/66
(b) 35/66
(c) 5/12
(d) 1/2
Answer: (a)
Explanation: Ways to get both red = C(5,2)=10. Both black = C(7,2)=21. Favourable =31. Total ways = C(12,2)=66. Probability =31/66.
Q24. If two events A and B are mutually exclusive, then P(A∩B) equals:
(a) P(A)+P(B)
(b) 0 (c) P(A)·P(B) (d) 1
Answer: (b)
Explanation: Mutually exclusive events cannot occur together, so their intersection is empty → probability 0.
Q25. A box contains 1 defective and 4 non‑defective bulbs. If three bulbs are selected at random with replacement, what is the probability that exactly one of them is defective?
(a) 96/125 (b) 48/125
(c) 12/125
(d) 36/125
Answer: (b) Explanation: P(defective)=1/5, P(good)=4/5. For exactly one defective in three trials: C(3,1)(1/5)(4/5)^2 = 3(1/5)(16/25)=48/125.
