1. The set of all possible outcomes of a random experiment is called:
A. Sample Space
B. Event Space
C. Outcome Set
D. Probability Field
Show Answer
Answer: A. Sample Space
Explanation: The collection of all possible outcomes of a random experiment is defined as its sample space (S).
2. If a coin is tossed 3 times, the number of elements in the sample space is:
Show Answer
Answer: A. 8
Explanation: Total outcomes = 2³ = 8.
3. An event having only one sample point is called a/an:
A. Simple Event
B. Compound Event
C. Impossible Event
D. Certain Event
Show Answer
Answer: A. Simple Event
Explanation: An event containing a single outcome of the sample space is called an elementary or simple event.
4. Two events A and B are mutually exclusive if:
A. A ∩ B = ∅
B. A ∪ B = S
C. A ∩ B = S
D. P(A) = P(B)
Show Answer
Answer: A. A ∩ B = ∅
Explanation: Mutually exclusive events cannot occur simultaneously, meaning their intersection is the empty set (∅).
5. Events A₁, A₂, ..., Aₙ are called exhaustive if:
A. A₁ ∪ A₂ ∪ ... ∪ Aₙ = S
B. A₁ ∩ A₂ ∩ ... ∩ Aₙ = ∅
C. P(A₁) + P(A₂) + ... + P(Aₙ) = 0
D. A₁ ∩ A₂ = ∅
Show Answer
Answer: A. A₁ ∪ A₂ ∪ ... ∪ Aₙ = S
Explanation: Events are exhaustive if their union equals the entire sample space S.
6. For any event A, the probability P(A) always satisfies:
A. 0 ≤ P(A) ≤ 1
B. -1 ≤ P(A) ≤ 1
C. 0 < P(A) < 1
D. P(A) ≥ 1
Show Answer
Answer: A. 0 ≤ P(A) ≤ 1
Explanation: Probability of any event lies between 0 and 1 inclusive.
7. The probability of an impossible event is:
Show Answer
Answer: A. 0
Explanation: An impossible event contains no sample points (∅), so its probability is 0.
8. The probability of a certain (sure) event is:
A. 1
B. 0
C. 1/2
D. Infinity
Show Answer
Answer: A. 1
Explanation: A sure event encompasses the complete sample space S, so P(S) = 1.
9. If P(A) is the probability of event A, then P(not A) or P(A') is:
A. 1 - P(A)
B. P(A) - 1
C. 1 / P(A)
D. P(A)
Show Answer
Answer: A. 1 - P(A)
Explanation: Since P(A) + P(A') = 1, P(A') = 1 - P(A).
10. For any two events A and B, P(A ∪ B) is given by:
A. P(A) + P(B) - P(A ∩ B)
B. P(A) + P(B) + P(A ∩ B)
C. P(A) × P(B)
D. P(A) - P(B)
Show Answer
Answer: A. P(A) + P(B) - P(A ∩ B)
Explanation: General addition theorem of probability: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
11. If A and B are mutually exclusive events, then P(A ∪ B) is equal to:
A. P(A) + P(B)
B. P(A) × P(B)
C. P(A) - P(B)
D. 0
Show Answer
Answer: A. P(A) + P(B)
Explanation: For mutually exclusive events, P(A ∩ B) = 0, so P(A ∪ B) = P(A) + P(B).
12. A die is thrown once. What is the probability of getting a prime number?
A. 1/2
B. 1/3
C. 2/3
D. 1/6
Show Answer
Answer: A. 1/2
Explanation: S = {1, 2, 3, 4, 5, 6}. Prime numbers = {2, 3, 5} (3 outcomes). P = 3/6 = 1/2.
13. Two dice are thrown simultaneously. Number of elements in the sample space is:
Show Answer
Answer: A. 36
Explanation: Total outcomes = 6 × 6 = 36.
14. Probability of drawing a king from a well-shuffled deck of 52 cards is:
A. 1/13
B. 1/52
C. 4/13
D. 1/26
Show Answer
Answer: A. 1/13
Explanation: Total kings = 4. P(King) = 4/52 = 1/13.
15. If P(A) = 0.4, P(B) = 0.7, and P(A ∩ B) = 0.3, then P(A ∪ B) is:
A. 0.8
B. 0.9
C. 1.1
D. 0.5
Show Answer
Answer: A. 0.8
Explanation: P(A ∪ B) = P(A) + P(B) - P(A ∩ B) = 0.4 + 0.7 - 0.3 = 0.8.
16. If A and B are mutually exclusive events with P(A) = 0.35 and P(B) = 0.45, then P(A ∪ B) is:
A. 0.80
B. 0.10
C. 0.1575
D. 0.70
Show Answer
Answer: A. 0.80
Explanation: Mutually exclusive means P(A ∩ B) = 0. So, P(A ∪ B) = 0.35 + 0.45 = 0.80.
17. What is the probability of getting a sum of 8 when two dice are thrown?
A. 5/36
B. 1/6
C. 4/36
D. 7/36
Show Answer
Answer: A. 5/36
Explanation: Pairs giving sum 8: (2,6), (3,5), (4,4), (5,3), (6,2) = 5 outcomes. P = 5/36.
18. Three coins are tossed. Probability of getting at least two heads is:
A. 1/2
B. 3/8
C. 5/8
D. 1/4
Show Answer
Answer: A. 1/2
Explanation: Outcomes with ≥ 2 heads: {HHH, HHT, HTH, THH} = 4 outcomes. Total = 8. P = 4/8 = 1/2.
19. In a single throw of a die, probability of getting a number greater than 4 is:
A. 1/3
B. 1/2
C. 2/3
D. 1/6
Show Answer
Answer: A. 1/3
Explanation: Numbers greater than 4 are {5, 6} (2 outcomes). P = 2/6 = 1/3.
20. Probability of getting 53 Sundays in a non-leap year is:
A. 1/7
B. 2/7
C. 53/365
D. 0
Show Answer
Answer: A. 1/7
Explanation: Non-leap year = 365 days = 52 weeks + 1 extra day. Probability that extra day is Sunday = 1/7.
21. Probability of getting 53 Sundays in a leap year is:
A. 2/7
B. 1/7
C. 53/366
D. 3/7
Show Answer
Answer: A. 2/7
Explanation: Leap year = 366 days = 52 weeks + 2 extra days. Pairs containing Sunday are (Sat, Sun) and (Sun, Mon) = 2/7.
22. Event "A but not B" in set notation is represented by:
A. A ∩ B'
B. A' ∩ B
C. A ∪ B'
D. (A ∪ B)'
Show Answer
Answer: A. A ∩ B'
Explanation: "A but not B" means elements belonging to A and not to B, denoted as A - B or A ∩ B'.
23. If P(A) = 0.6 and P(A ∩ B) = 0.2, then P(A ∩ B') is:
A. 0.4
B. 0.8
C. 0.3
D. 0.12
Show Answer
Answer: A. 0.4
Explanation: P(A ∩ B') = P(A) - P(A ∩ B) = 0.6 - 0.2 = 0.4.
24. If a card is drawn from a deck of 52 cards, probability that it is a red card or a king is:
A. 7/13
B. 1/2
C. 15/26
D. 6/13
Show Answer
Answer: A. 7/13
Explanation: P(Red) = 26/52, P(King) = 4/52, P(Red King) = 2/52. P = (26 + 4 - 2)/52 = 28/52 = 7/13.
25. If P(A) = 2/11, probability of event 'not A' is:
A. 9/11
B. 2/11
C. 11/2
D. 1/11
Show Answer
Answer: A. 9/11
Explanation: P(not A) = 1 - P(A) = 1 - 2/11 = 9/11.
26. Which of the following CANNOT be the probability of an event?
A. -1.5
B. 0.6
C. 2/3
D. 15%
Show Answer
Answer: A. -1.5
Explanation: Probability cannot be negative (0 ≤ P(E) ≤ 1).
27. A box contains 3 red and 5 black balls. One ball is drawn at random. Probability that it is red is:
A. 3/8
B. 5/8
C. 3/5
D. 1/8
Show Answer
Answer: A. 3/8
Explanation: Total balls = 8, Red balls = 3. P(Red) = 3/8.
28. Two events A and B are mutually exclusive and exhaustive. If P(A) = 3/5, then P(B) is:
A. 2/5
B. 3/5
C. 1/5
D. 0
Show Answer
Answer: A. 2/5
Explanation: Mutually exclusive & exhaustive means P(A) + P(B) = 1 ⇒ P(B) = 1 - 3/5 = 2/5.
29. In a simultaneous throw of two coins, probability of getting at most one head is:
A. 3/4
B. 1/2
C. 1/4
D. 2/3
Show Answer
Answer: A. 3/4
Explanation: Outcomes: {HH, HT, TH, TT}. At most one head = {HT, TH, TT} = 3 outcomes. P = 3/4.
30. If A and B are two events such that P(A ∪ B) = 1, then A and B are:
A. Exhaustive events
B. Mutually exclusive events
C. Independent events
D. Impossible events
Show Answer
Answer: A. Exhaustive events
Explanation: By definition, events whose union equals the sample space (P(A ∪ B) = P(S) = 1) are exhaustive events.