1. If P(E) is the probability of an event E, then which of the following is true?
A. 0 ≤ P(E) ≤ 1
B. 0 < P(E) < 1
C. -1 ≤ P(E) ≤ 1
D. P(E) > 1
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Answer: A. 0 ≤ P(E) ≤ 1
Explanation: The probability of any event always lies between 0 and 1 inclusive.
2. The probability of an impossible event is:
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Answer: B. 0
Explanation: An event that cannot occur has a probability of 0.
3. The probability of a sure or certain event is:
A. 0
B. 1
C. Infinity
D. 0.5
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Answer: B. 1
Explanation: An event that is guaranteed to happen has a probability equal to 1.
4. Which of the following CANNOT be the probability of an event?
A. 2 / 3
B. -1.5
C. 15%
D. 0.7
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Answer: B. -1.5
Explanation: Probability can never be negative. Therefore, -1.5 cannot be a probability.
5. If P(E) = 0.05, then the probability of 'not E', P(Ē), is:
A. 0.95
B. 0.05
C. 1.05
D. 0.90
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Answer: A. 0.95
Explanation: P(Ē) = 1 - P(E) = 1 - 0.05 = 0.95.
6. A single die is thrown once. Probability of getting a prime number is:
A. 1 / 2
B. 1 / 3
C. 1 / 6
D. 2 / 3
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Answer: A. 1 / 2
Explanation: Prime numbers on a die are {2, 3, 5} (3 outcomes). Total outcomes = 6. Probability = 3 / 6 = 1 / 2.
7. A card is drawn from a well-shuffled deck of 52 playing cards. The probability of getting a face card is:
A. 3 / 13
B. 1 / 13
C. 4 / 13
D. 9 / 52
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Answer: A. 3 / 13
Explanation: Number of face cards (J, Q, K) = 12. Probability = 12 / 52 = 3 / 13.
8. The probability of getting a king of red colour from a well-shuffled deck of 52 cards is:
A. 1 / 26
B. 1 / 13
C. 2 / 13
D. 1 / 52
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Answer: A. 1 / 26
Explanation: There are 2 red kings (King of Hearts and King of Diamonds). Probability = 2 / 52 = 1 / 26.
9. Probability of getting a sum of 12 when two dice are thrown together is:
A. 1 / 36
B. 1 / 18
C. 1 / 6
D. 5 / 36
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Answer: A. 1 / 36
Explanation: Favourable outcome is only (6, 6). Total outcomes when 2 dice thrown = 36. Probability = 1 / 36.
10. A bag contains 3 red balls and 5 black balls. A ball is drawn at random. Probability that it is red is:
A. 3 / 8
B. 5 / 8
C. 3 / 5
D. 1 / 2
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Answer: A. 3 / 8
Explanation: Total balls = 3 + 5 = 8. Red balls = 3. Probability = 3 / 8.
11. Probability that a leap year chosen at random contains 53 Sundays is:
A. 2 / 7
B. 1 / 7
C. 53 / 366
D. 26 / 52
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Answer: A. 2 / 7
Explanation: A leap year has 366 days = 52 weeks + 2 extra days. Out of 7 combinations for 2 days, 2 contain Sunday. Probability = 2 / 7.
12. Probability that a non-leap year contains 53 Mondays is:
A. 1 / 7
B. 2 / 7
C. 53 / 365
D. 1 / 365
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Answer: A. 1 / 7
Explanation: Non-leap year has 365 days = 52 weeks + 1 extra day. Probability that this 1 day is Monday = 1 / 7.
13. Probability of getting at least one head when two coins are tossed simultaneously is:
A. 3 / 4
B. 1 / 4
C. 1 / 2
D. 1
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Answer: A. 3 / 4
Explanation: Outcomes = {HH, HT, TH, TT}. At least one head occurs in {HH, HT, TH} (3 cases). Probability = 3 / 4.
14. Sum of probabilities of all elementary events of an experiment is equal to:
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Answer: A. 1
Explanation: Fundamental property of probability: Sum of all elementary probabilities is always 1.
15. If the probability of winning a game is 0.7, then probability of losing it is:
A. 0.3
B. 0.7
C. 0.4
D. 0.1
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Answer: A. 0.3
Explanation: P(Losing) = 1 - P(Winning) = 1 - 0.7 = 0.3.
16. A letter is chosen at random from English alphabets. Probability that it is a vowel is:
A. 5 / 26
B. 21 / 26
C. 1 / 26
D. 5 / 21
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Answer: A. 5 / 26
Explanation: Vowels = {A, E, I, O, U} = 5. Total letters = 26. Probability = 5 / 26.
17. In a simultaneous throw of two dice, probability of getting a doublet is:
A. 1 / 6
B. 1 / 36
C. 5 / 36
D. 1 / 12
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Answer: A. 1 / 6
Explanation: Doublets = {(1,1), (2,2), (3,3), (4,4), (5,5), (6,6)} = 6. Total = 36. Probability = 6 / 36 = 1 / 6.
18. A number is selected from first 20 natural numbers. Probability that it is a prime number is:
A. 2 / 5
B. 1 / 2
C. 9 / 20
D. 3 / 10
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Answer: A. 2 / 5
Explanation: Primes ≤ 20: {2, 3, 5, 7, 11, 13, 17, 19} = 8. Probability = 8 / 20 = 2 / 5.
19. A box contains 90 discs numbered 1 to 90. If one disc is drawn, probability of getting a two-digit number is:
A. 9 / 10
B. 1 / 10
C. 8 / 9
D. 81 / 100
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Answer: A. 9 / 10
Explanation: Single-digit numbers (1-9) = 9. Two-digit numbers = 90 - 9 = 81. Probability = 81 / 90 = 9 / 10.
20. When three unbiased coins are tossed, probability of getting at most two heads is:
A. 7 / 8
B. 3 / 8
C. 1 / 2
D. 1 / 8
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Answer: A. 7 / 8
Explanation: Outcomes with at most 2 heads = all outcomes except HHH = 8 - 1 = 7. Probability = 7 / 8.
21. Probability that a number selected at random from 1 to 30 is a multiple of 5 is:
A. 1 / 5
B. 1 / 6
C. 1 / 3
D. 2 / 5
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Answer: A. 1 / 5
Explanation: Multiples of 5 from 1 to 30 are {5, 10, 15, 20, 25, 30} = 6. Probability = 6 / 30 = 1 / 5.
22. The probability of getting a number greater than 6 on a ordinary six-faced die is:
A. 0
B. 1
C. 1 / 6
D. 2 / 3
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Answer: A. 0
Explanation: Numbers on a die are 1 to 6. No number is greater than 6, so probability = 0.
23. Probability of drawing an Ace from a well-shuffled deck of 52 cards is:
A. 1 / 13
B. 1 / 52
C. 4 / 13
D. 1 / 26
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Answer: A. 1 / 13
Explanation: Number of Aces in a deck = 4. Probability = 4 / 52 = 1 / 13.
24. If two dice are thrown together, probability that sum of numbers is less than 13 is:
A. 1
B. 0
C. 1 / 2
D. 35 / 36
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Answer: A. 1
Explanation: Maximum sum possible on 2 dice is 6 + 6 = 12, which is always less than 13. It is a sure event (P = 1).
25. A box contains 5 red, 8 white, and 4 green marbles. Probability that marble drawn is NOT green is:
A. 13 / 17
B. 4 / 17
C. 5 / 17
D. 8 / 17
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Answer: A. 13 / 17
Explanation: Total marbles = 5 + 8 + 4 = 17. Non-green marbles = 5 + 8 = 13. Probability = 13 / 17.
26. Probability of getting an odd number in a single throw of a die is:
A. 1 / 2
B. 1 / 3
C. 2 / 3
D. 1 / 6
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Answer: A. 1 / 2
Explanation: Odd numbers on a die = {1, 3, 5} = 3. Probability = 3 / 6 = 1 / 2.
27. Two coins are tossed simultaneously. Probability of getting 2 tails is:
A. 1 / 4
B. 1 / 2
C. 3 / 4
D. 1
Show Answer
Answer: A. 1 / 4
Explanation: Outcomes = {HH, HT, TH, TT}. Outcome with 2 tails = {TT} (1 case). Probability = 1 / 4.
28. Total number of outcomes when two dice are rolled together is:
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Answer: A. 36
Explanation: Each die has 6 outcomes. Total outcomes for 2 dice = 6 × 6 = 36.
29. If P(A) = 0.35, then P(not A) is equal to:
A. 0.65
B. 0.35
C. 0.55
D. 0.75
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Answer: A. 0.65
Explanation: P(not A) = 1 - P(A) = 1 - 0.35 = 0.65.
30. Probability of an event can be expressed in percentage as:
A. Any percentage from 0% to 100%
B. Any percentage greater than 100%
C. Less than 0%
D. Exactly 50% only
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Answer: A. Any percentage from 0% to 100%
Explanation: Since probability ranges from 0 to 1, in percentage terms it ranges from 0% to 100%.