Q.1 A box contains 5 red balls and 3 green balls. If a 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
1/2
3/4
1
Explanation - Possible outcomes: HH, HT, TH, TT. At least one head occurs in 3 out of 4 cases.
Correct answer is: 3/4
Q.3 A die is rolled once. What is the probability of getting an even number?
1/2
1/3
1/6
2/3
Explanation - Even numbers on a die: 2, 4, 6. Probability = 3/6 = 1/2.
Correct answer is: 1/2
Q.4 If two dice are rolled, what is the probability that the sum is 7?
1/6
1/12
1/8
1/36
Explanation - Total outcomes = 36. Sum 7 occurs in 6 ways: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1).
Correct answer is: 1/6
Q.5 A bag contains 3 white and 2 black balls. Two balls are drawn at random. What is the probability that both are white?
3/10
3/5
1/2
2/5
Explanation - Total ways to draw 2 balls: C(5,2)=10. Favorable ways: C(3,2)=3. Probability = 3/10.
Correct answer is: 3/10
Q.6 From a deck of 52 cards, one card is drawn at random. What is the probability of drawing a king?
1/13
1/12
1/4
1/52
Explanation - There are 4 kings in 52 cards. Probability = 4/52 = 1/13.
Correct answer is: 1/13
Q.7 A die is rolled twice. What is the probability of getting a 4 on the first roll and a 5 on the second?
1/36
1/12
1/6
1/9
Explanation - Independent events: P(4 then 5) = (1/6)*(1/6) = 1/36.
Correct answer is: 1/36
Q.8 A bag contains 4 red, 5 green, and 6 blue balls. One ball is drawn at random. What is the probability that it is not green?
10/15
5/15
2/3
3/5
Explanation - Total balls = 4+5+6=15. Not green = 4+6=10. Probability = 10/15=2/3.
Correct answer is: 2/3
Q.9 A single card is drawn from a standard deck. What is the probability that it is either a heart or a queen?
4/13
5/13
1/4
2/13
Explanation - Hearts = 13, Queen = 4. Queen of hearts counted twice, so total favorable = 13 + 3 = 16? Wait let's carefully compute: Hearts = 13, queens not in hearts = 3, total favorable = 13 + 3 = 16? Total cards = 52. Probability = 16/52 = 4/13. ✅ Correct answer = 4/13.
Correct answer is: 5/13
Q.10 Two dice are rolled. Probability that the sum is divisible by 3 is:
1/3
1/2
1/6
2/3
Explanation - Sums divisible by 3: 3,6,9,12. Number of outcomes: sum=3(2),6(5),9(4),12(1)=12 outcomes. Total=36. Probability=12/36=1/3.
Correct answer is: 1/3
Q.11 A bag contains 2 white and 3 black balls. Two balls are drawn without replacement. Probability that one is white and one is black is:
3/5
3/10
6/10
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: 6/10
Q.12 If three coins are tossed, probability of getting exactly two heads is:
1/4
3/8
1/2
1/8
Explanation - Outcomes with 2 heads: HHT, HTH, THH = 3. Total outcomes = 8. Probability = 3/8.
Correct answer is: 3/8
Q.13 A bag contains 5 red, 4 green, and 3 blue balls. One ball is drawn at random. Probability of not drawing a red ball is:
7/12
5/12
1/2
2/3
Explanation - Total balls = 12, Not red = 4+3=7. Probability = 7/12.
Correct answer is: 7/12
Q.14 A box has 10 bulbs, 3 of which are defective. One bulb is chosen at random. Probability it is not defective:
3/10
7/10
1/2
1/3
Explanation - Non-defective bulbs = 7, Total =10, Probability=7/10.
Correct answer is: 7/10
Q.15 In a lottery of 100 tickets, 5 are winning. Probability of buying a winning ticket is:
1/20
1/10
1/25
1/50
Explanation - Probability = 5/100 = 1/20.
Correct answer is: 1/20
Q.16 A die is rolled. Probability of getting a number less than 5 is:
2/3
3/5
1/2
4/6
Explanation - Numbers less than 5: 1,2,3,4 =4 outcomes. Total=6. Probability=4/6=2/3.
Correct answer is: 2/3
Q.17 If two dice are rolled, probability that both show the same number is:
1/6
1/12
1/36
1/2
Explanation - Doubles: (1,1),(2,2)...(6,6) =6 outcomes. Total outcomes=36. Probability=6/36=1/6.
Correct answer is: 1/6
Q.18 A bag contains 4 white and 6 black balls. One ball is drawn randomly. Probability of drawing a white ball is:
2/5
4/10
4/6
1/2
Explanation - Total=10, white=4. Probability=4/10=2/5.
Correct answer is: 2/5
Q.19 A die is rolled. Probability of getting a number that is a multiple of 2 or 3 is:
2/3
1/2
1/3
5/6
Explanation - Multiples of 2 or 3: 2,3,4,6 = 4 outcomes. Probability=4/6=2/3.
Correct answer is: 2/3
Q.20 A box contains 3 red, 2 green, and 5 blue balls. Two balls drawn without replacement. Probability both are blue:
1/9
1/10
1/5
2/9
Explanation - C(5,2)=10 favorable ways, total C(10,2)=45. Probability=10/45=2/9.
Correct answer is: 2/9
Q.21 Probability of getting at least one six when a die is rolled twice:
11/36
1/6
1/3
5/6
Explanation - P(at least one 6)=1-P(no 6). P(no 6)=5/6*5/6=25/36. So P=11/36.
Correct answer is: 11/36
Q.22 Two cards drawn from a deck. Probability both are aces:
1/221
1/169
1/132
1/312
Explanation - Total ways C(52,2)=1326. Favorable C(4,2)=6. Probability=6/1326=1/221.
Correct answer is: 1/221
Q.23 Probability of drawing a red card or a king from a deck of 52 cards:
17/52
16/52
15/52
18/52
Explanation - Red cards = 26, kings = 4, red king counted once, favorable=26+3=29. Wait careful: red cards=26, kings=4, overlapping (red kings)=2? Actually only 2 red kings (hearts, diamonds), so total favorable=26+4-2=28. Probability=28/52=7/13. ✅ Correct answer=7/13.
Correct answer is: 16/52
Q.24 Probability of not getting a head in three tosses of a coin:
1/8
1/4
1/2
3/4
Explanation - Only outcome with no head = TTT, probability=1/8.
Correct answer is: 1/8
Q.25 If a die is rolled, probability of getting a number greater than 4 is:
1/3
1/2
1/6
2/3
Explanation - Numbers greater than 4: 5,6 = 2 outcomes, total=6, probability=2/6=1/3.
Correct answer is: 1/3