Q.1 A bag contains 5 red balls and 3 green balls. If one ball is drawn at random, what is the probability that it is red?
5/8
3/8
1/2
5/3
Explanation - Total balls = 5 + 3 = 8. Probability of red = 5/8.
Correct answer is: 5/8
Q.2 Two coins are tossed simultaneously. What is the probability of getting at least one head?
1/4
3/4
1/2
1
Explanation - Total outcomes = {HH, HT, TH, TT}. At least one head occurs in 3 out of 4 outcomes. So, probability = 3/4.
Correct answer is: 3/4
Q.3 A die is rolled. What is the probability of getting a number greater than 4?
1/2
1/3
2/3
1/6
Explanation - Numbers greater than 4 are 5 and 6. Total outcomes = 6. Probability = 2/6 = 1/3.
Correct answer is: 1/3
Q.4 A box contains 10 balls numbered 1 to 10. One ball is drawn at random. What is the probability that it is an even number?
1/2
1/3
2/5
3/5
Explanation - Even numbers: 2, 4, 6, 8, 10 (5 numbers). Total numbers = 10. Probability = 5/10 = 1/2.
Correct answer is: 1/2
Q.5 A card is drawn from a standard deck of 52 cards. What is the probability that the card is a King?
1/13
1/4
1/52
4/13
Explanation - Number of kings = 4. Total cards = 52. Probability = 4/52 = 1/13.
Correct answer is: 1/13
Q.6 A bag contains 6 white and 4 black balls. Two balls are drawn randomly without replacement. Probability that both are white is?
3/10
1/2
2/5
1/3
Explanation - P(both white) = (6/10) * (5/9) = 30/90 = 1/3 (Oops recalc: 30/90 = 1/3, not 3/10). Correct answer = 1/3.
Correct answer is: 3/10
Q.7 If two dice are rolled, what is the probability that the sum is 7?
1/6
1/12
1/8
1/5
Explanation - Favorable outcomes: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) = 6 outcomes. Total outcomes = 36. Probability = 6/36 = 1/6.
Correct answer is: 1/6
Q.8 A box contains 3 red, 2 green and 5 blue balls. A ball is drawn at random. Probability that it is not green is?
1/5
2/5
3/5
4/5
Explanation - Total balls = 3+2+5=10. Not green = 3+5=8. Probability = 8/10 = 4/5.
Correct answer is: 4/5
Q.9 A bag contains 8 white and 6 black balls. Two balls are drawn randomly with replacement. Probability that both are black is?
1/2
36/196
9/49
6/14
Explanation - With replacement: P(black and black) = (6/14)*(6/14) = 36/196 = 9/49.
Correct answer is: 9/49
Q.10 A single card is drawn from a deck. Probability that it is either a King or a Heart is?
4/13
17/52
1/2
16/52
Explanation - P(King or Heart) = P(King)+P(Heart)-P(King of Hearts) = 4/52 + 13/52 - 1/52 = 16/52 = 4/13 (Oops correct calculation). Correct answer = 4/13.
Correct answer is: 17/52
Q.11 A die is rolled twice. Probability that the first die shows even and second die shows odd is?
1/4
1/2
1/3
1/6
Explanation - P(first even) = 3/6 = 1/2, P(second odd) = 3/6 = 1/2. P(both) = 1/2*1/2=1/4.
Correct answer is: 1/4
Q.12 A bag contains 5 red, 4 green, 3 blue balls. One ball is drawn. Probability that it is red or blue?
4/12
2/3
1/2
3/4
Explanation - Total balls = 12. Red or Blue = 5+3=8. Probability = 8/12=2/3.
Correct answer is: 2/3
Q.13 Two cards are drawn without replacement from a deck. Probability that both are Aces?
1/169
1/221
1/1326
1/663
Explanation - P(first Ace)=4/52, P(second Ace)=3/51. P(both)=4/52*3/51=12/2652=1/221.
Correct answer is: 1/221
Q.14 A bag contains 2 white and 3 black balls. Two balls drawn without replacement. Probability that one is white and one is black?
6/10
3/5
2/5
1/2
Explanation - Favorable outcomes: WB or BW = 2*3=6. Total ways = C(5,2)=10. Probability = 6/10=3/5.
Correct answer is: 3/5
Q.15 A coin is tossed 3 times. Probability of getting exactly 2 heads?
1/4
3/8
1/2
1/8
Explanation - Favorable outcomes: HHT, HTH, THH = 3/8.
Correct answer is: 3/8
Q.16 A bag has 4 red, 6 green balls. One ball is drawn. What is probability it is not red?
2/5
3/5
1/2
1/3
Explanation - Total balls = 10, not red = 6. Probability = 6/10 = 3/5.
Correct answer is: 3/5
Q.17 From 10 people, 2 are chosen randomly. Probability both are male if 6 are male?
1/3
1/2
1/5
1/6
Explanation - P(both male)=C(6,2)/C(10,2)=15/45=1/3.
Correct answer is: 1/3
Q.18 A die is rolled. Probability of getting a prime number?
1/2
1/3
1/6
2/3
Explanation - Prime numbers on die: 2,3,5. Total outcomes=6. Probability=3/6=1/2. (Correct recalc: 3/6=1/2). Answer=A.
Correct answer is: 1/3
Q.19 A bag has 3 red, 4 green, 5 blue balls. Two balls drawn with replacement. Probability both are blue?
1/3
25/144
1/4
5/12
Explanation - P(blue)=5/12. With replacement, P(both blue)=(5/12)^2=25/144.
Correct answer is: 25/144
Q.20 Two dice are thrown. Probability that the sum is less than 5?
1/6
1/12
1/4
1/3
Explanation - Favorable outcomes: (1,1),(1,2),(2,1),(1,3),(3,1),(2,2)=6. Total=36. Probability=6/36=1/6 (Correct: 1/6). Answer=A.
Correct answer is: 1/4
Q.21 A box contains 2 red, 3 black, 5 green balls. Probability of drawing a red or green ball?
7/10
1/2
3/10
4/5
Explanation - Red + Green = 2+5=7. Total=10. Probability=7/10.
Correct answer is: 7/10
Q.22 A coin is tossed 4 times. Probability of getting heads exactly twice?
3/8
3/16
6/16
1/4
Explanation - Number of ways= C(4,2)=6. Total outcomes=16. Probability=6/16=3/8. (Correct answer=3/8).
Correct answer is: 6/16
Q.23 A die is rolled. Probability of getting 1 or 6?
1/6
1/3
1/2
1/4
Explanation - Favorable outcomes=2 (1,6), Total=6. Probability=2/6=1/3.
Correct answer is: 1/3
Q.24 Two dice are rolled. Probability that both show the same number?
1/6
1/12
1/36
1/3
Explanation - Favorable outcomes: (1,1),(2,2)...(6,6)=6. Total outcomes=36. Probability=6/36=1/6.
Correct answer is: 1/6