Q.1 If a coin is tossed twice, what is the probability of getting exactly one head?
1/4
1/2
1/3
3/4
Explanation - Sample space = {HH, HT, TH, TT}. Exactly one head occurs in HT and TH, so probability = 2/4 = 1/2.
Correct answer is: 1/2
Q.2 A die is rolled. What is the probability of getting a number greater than 4?
1/6
1/3
1/2
2/3
Explanation - Numbers greater than 4 are 5 and 6. So probability = 2/6 = 1/3.
Correct answer is: 1/3
Q.3 Two dice are rolled. What is the probability that the sum is 7?
1/6
1/8
1/12
1/36
Explanation - Favorable outcomes for sum 7: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1). Total outcomes = 36. Probability = 6/36 = 1/6.
Correct answer is: 1/6
Q.4 A bag contains 3 red, 4 blue, and 5 green balls. One ball is drawn at random. What is the probability it is not red?
3/12
9/12
1/3
2/3
Explanation - Total balls = 12. Balls not red = 4 + 5 = 9. Probability = 9/12 = 3/4.
Correct answer is: 9/12
Q.5 If two coins are tossed simultaneously, what is the probability of getting at least one tail?
1/4
1/2
3/4
1
Explanation - Sample space = {HH, HT, TH, TT}. At least one tail occurs in HT, TH, TT, so probability = 3/4.
Correct answer is: 3/4
Q.6 A card is drawn from a standard deck of 52 cards. Probability of getting a King is?
1/13
1/4
1/12
1/52
Explanation - There are 4 Kings in 52 cards. Probability = 4/52 = 1/13.
Correct answer is: 1/13
Q.7 If two dice are rolled, probability that both dice show odd numbers is?
1/2
1/4
1/3
1/6
Explanation - Odd numbers on a die: 1,3,5 (3/6 = 1/2 for one die). Probability both odd = 1/2 * 1/2 = 1/4.
Correct answer is: 1/4
Q.8 A box contains 5 white and 3 black balls. Two balls are drawn randomly. Probability both are white is?
5/8
1/2
5/14
5/28
Explanation - Total ways to draw 2 balls: C(8,2)=28. Favorable ways for 2 white: C(5,2)=10. Probability = 10/28 = 5/14.
Correct answer is: 5/14
Q.9 In a class of 40 students, 25 like Math, 20 like Science, and 10 like both. Probability a randomly chosen student likes Math or Science?
35/40
30/40
25/40
20/40
Explanation - P(Math ∪ Science) = P(Math)+P(Science)-P(Math ∩ Science) = 25+20-10=35. Probability = 35/40.
Correct answer is: 35/40
Q.10 A fair coin is tossed 3 times. Probability of getting at least two heads?
1/2
1/4
3/8
1/8
Explanation - Sample space outcomes with ≥2 heads: HHT, HTH, THH, HHH (4 outcomes). Total outcomes = 8. Probability = 4/8 = 1/2.
Correct answer is: 1/2
Q.11 A die is rolled twice. Probability that the first die shows 2 and second shows 5?
1/12
1/36
1/6
1/18
Explanation - Probability first die is 2 = 1/6, second die is 5 = 1/6. Combined probability = 1/6 * 1/6 = 1/36.
Correct answer is: 1/36
Q.12 Two cards are drawn without replacement from a deck of 52. Probability both are Aces?
1/169
1/221
1/1326
1/78
Explanation - Total ways = C(52,2)=1326. Favorable = C(4,2)=6. Probability = 6/1326 = 1/221.
Correct answer is: 1/221
Q.13 A bag contains 2 red, 3 green, and 5 blue balls. One ball is drawn. Probability it is not green?
1/2
2/5
7/10
3/5
Explanation - Total balls = 10. Not green = 2+5=7. Probability = 7/10.
Correct answer is: 7/10
Q.14 A box contains 4 defective and 6 non-defective bulbs. One bulb is chosen at random. Probability it is defective?
2/5
3/5
4/5
1/2
Explanation - Total bulbs = 10. Defective = 4. Probability = 4/10 = 2/5.
Correct answer is: 2/5
Q.15 If a die is thrown, probability of getting a prime number?
1/2
1/3
1/6
2/3
Explanation - Prime numbers on a die: 2,3,5 (3 numbers). Probability = 3/6 = 1/2.
Correct answer is: 1/2
Q.16 A bag contains 7 red and 5 green balls. Two balls are drawn randomly with replacement. Probability both are red?
7/12
49/144
1/2
7/24
Explanation - Probability first red = 7/12, second red = 7/12 (with replacement). Combined probability = 7/12 * 7/12 = 49/144.
Correct answer is: 49/144
Q.17 If two coins are tossed, probability of getting the same face on both coins?
1/2
1/4
3/4
1/3
Explanation - Same face occurs in HH, TT. Total outcomes = 4. Probability = 2/4 = 1/2.
Correct answer is: 1/2
Q.18 A die is rolled once. Probability of not getting a 1?
1/6
5/6
1/2
2/3
Explanation - Total outcomes = 6. Favorable outcomes = 2,3,4,5,6 (5 outcomes). Probability = 5/6.
Correct answer is: 5/6
Q.19 A bag has 3 white and 2 black balls. Two balls are drawn randomly. Probability one is white and one is black?
3/10
1/2
3/5
1/5
Explanation - Favorable outcomes: WB, BW = 3*2 + 2*3 = 12 combinations. Total outcomes = C(5,2)=10. Probability = 6/10 = 3/5.
Correct answer is: 3/5
Q.20 Probability of selecting a vowel from English alphabet?
5/26
1/5
5/21
1/26
Explanation - Vowels = A, E, I, O, U (5 out of 26 letters). Probability = 5/26.
Correct answer is: 5/26
Q.21 Two dice are rolled. Probability that sum is even?
1/2
1/3
1/4
2/3
Explanation - Sum even occurs when both dice are even or both odd. Probability = 1/4 + 1/4 = 1/2.
Correct answer is: 1/2
Q.22 A bag contains 5 red, 3 blue, 2 green balls. One ball is drawn. Probability of not blue or green?
1/2
1/5
1/3
1/10
Explanation - Not blue or green = red balls = 5. Total balls = 10. Probability = 5/10 = 1/2.
Correct answer is: 1/2
Q.23 A coin is tossed 4 times. Probability of getting exactly two heads?
3/8
6/16
1/2
1/4
Explanation - Number of ways to get 2 heads in 4 tosses = C(4,2)=6. Total outcomes = 2^4=16. Probability = 6/16.
Correct answer is: 6/16
Q.24 Probability of drawing a red card or a King from a deck of 52 cards?
17/52
1/2
4/13
9/26
Explanation - Red cards = 26, Kings = 4, but 2 red kings counted twice. Probability = (26+4-2)/52 = 28/52=17/52.
Correct answer is: 17/52