Chapter-14 Probability — Online MCQ Test
MATHS · CLASS 11 FIRST PUC · Karnataka State Board
Practice Chapter-14 Probability with a free chapter-wise online MCQ test.
This chapter covers: Random experiment - Sample space - Outcomes - Events - Impossible event - Sure event - Mutually exclusive events - Exhaustive events - Axiomatic approach to probability.
AI-generated questions from basic to board-exam level, with instant results and explanations.
Chapter-14 Probability — Important Questions & Answers
What is a random experiment?
- A. An experiment whose outcome is certain before performing it
- B. An experiment whose outcome cannot be predicted with certainty, though the set of all possible outcomes is known
- C. An experiment that always gives the same result
- D. An experiment performed with a specific purpose to get a predetermined outcome
Answer: B. An experiment whose outcome cannot be predicted with certainty, though the set of all possible outcomes is known
A random experiment is characterized by uncertainty in its individual outcome, but all possible outcomes are known beforehand.
A random experiment is characterized by uncertainty in its individual outcome, but all possible outcomes are known beforehand.
The sample space of rolling a die is:
- A. {1, 2, 3, 4, 5}
- B. {0, 1, 2, 3, 4, 5, 6}
- C. {1, 2, 3, 4, 5, 6}
- D. {2, 4, 6}
Answer: C. {1, 2, 3, 4, 5, 6}
A die has 6 faces numbered 1 to 6, so the sample space contains all these 6 outcomes.
A die has 6 faces numbered 1 to 6, so the sample space contains all these 6 outcomes.
Which of the following is an outcome in the context of probability?
- A. The result of a single performance of a random experiment
- B. All possible results of an experiment
- C. A favorable result that must occur
- D. The probability of an event happening
Answer: A. The result of a single performance of a random experiment
An outcome is a single result that occurs when a random experiment is performed once.
An outcome is a single result that occurs when a random experiment is performed once.
What is an event in probability?
- A. Any single result of an experiment
- B. A subset of the sample space
- C. The total number of outcomes
- D. The certainty of an outcome
Answer: B. A subset of the sample space
An event is defined as any subset of the sample space, which can contain one or more outcomes.
An event is defined as any subset of the sample space, which can contain one or more outcomes.
When tossing two coins, how many elements are in the sample space?
- A. 2
- B. 3
- C. 4
- D. 8
Answer: C. 4
The sample space is {HH, HT, TH, TT}, which contains 4 equally likely outcomes.
The sample space is {HH, HT, TH, TT}, which contains 4 equally likely outcomes.
In rolling a die, the event 'getting a number less than 7' is:
- A. An impossible event
- B. A sure event
- C. A simple event
- D. A compound event
Answer: B. A sure event
Since all outcomes (1, 2, 3, 4, 5, 6) are less than 7, this event is certain to occur, making it a sure event.
Since all outcomes (1, 2, 3, 4, 5, 6) are less than 7, this event is certain to occur, making it a sure event.
If A and B are mutually exclusive and exhaustive events, which is true?
- A. P(A) + P(B) = 0
- B. P(A) + P(B) = 1
- C. P(A ∩ B) = 1
- D. P(A ∪ B) = 0
Answer: B. P(A) + P(B) = 1
Mutually exclusive means A ∩ B = ∅; exhaustive means A ∪ B = S. Therefore, P(A) + P(B) = P(A ∪ B) = P(S) = 1.
Mutually exclusive means A ∩ B = ∅; exhaustive means A ∪ B = S. Therefore, P(A) + P(B) = P(A ∪ B) = P(S) = 1.
In a sample space S, if events A, B, and C partition S (are mutually exclusive and exhaustive), and P(A) = 0.3, P(B) = 0.5, then P(C) is:
- A. 0.2
- B. 0.8
- C. 0.15
- D. Cannot be determined
Answer: A. 0.2
Since A, B, C partition S: P(A) + P(B) + P(C) = 1, so P(C) = 1 - 0.3 - 0.5 = 0.2.
Since A, B, C partition S: P(A) + P(B) + P(C) = 1, so P(C) = 1 - 0.3 - 0.5 = 0.2.
Consider the sample space of outcomes from spinning a spinner twice. If the first spin gives outcome 'a' with probability 0.3 and outcome 'b' with probability 0.7, and the second spin is independent with the same probabilities, what is P(both spins show 'a')?
- A. 0.6
- B. 0.09
- C. 0.3
- D. 0.49
Answer: B. 0.09
Since spins are independent, P(a then a) = P(a) × P(a) = 0.3 × 0.3 = 0.09.
Since spins are independent, P(a then a) = P(a) × P(a) = 0.3 × 0.3 = 0.09.
A probability measure P on a sample space S must satisfy which of the following conditions (selecting the most complete answer)?
- A. 0 ≤ P(A) ≤ 1 for all events A, and P(S) = 1
- B. P(A) ≥ 0 for all events A, P(S) = 1, and P(A ∪ B) = P(A) + P(B) for mutually exclusive events
- C. 0 ≤ P(A) ≤ 1, P(∅) = 0, P(S) = 1, and P(A') = 1 - P(A)
- D. All of the above conditions together form the axiomatic definition
Answer: D. All of the above conditions together form the axiomatic definition
The axiomatic approach to probability includes all three axioms and the derived properties listed. Option D correctly identifies that all stated conditions collectively define a probability measure.
The axiomatic approach to probability includes all three axioms and the derived properties listed. Option D correctly identifies that all stated conditions collectively define a probability measure.