Class 12 Mathematics (NCERT)

1. The conditional probability P(A|B) is defined as:

• A. P(A∩B) / P(B), provided P(B) ≠ 0
• B. P(A) + P(B)
• C. P(A) · P(B)
• D. P(A) - P(B)

2. Two events A and B are said to be independent if:

• A. P(A∩B) = P(A) · P(B)
• B. P(A∩B) = P(A) + P(B)
• C. P(A|B) = 0
• D. A and B are mutually exclusive

3. Bayes' theorem is primarily used to find:

• A. The probability of a cause given an observed effect
• B. The probability of independent events only
• C. The mean of a probability distribution
• D. The variance of a probability distribution

4. A random variable that can take only specific, countable values is called a:

• A. Discrete random variable
• B. Continuous random variable
• C. Independent variable
• D. Dependent variable, without further qualification

5. The probability distribution of a discrete random variable must satisfy the condition that:

• A. The sum of all the probabilities equals 1
• B. The sum of all the probabilities equals 0
• C. Each individual probability equals 1
• D. Probabilities can take negative values

6. The mean (expectation) of a discrete random variable X is given by:

• A. E(X) = Σ x · P(x)
• B. E(X) = Σ P(x)
• C. E(X) = Σ x
• D. E(X) = x · n

7. Two events are called mutually exclusive if:

• A. They cannot occur simultaneously, i.e., A∩B = ∅
• B. They always occur together
• C. They are statistically independent
• D. Their individual probabilities are equal

8. The Binomial distribution is applicable in situations involving:

• A. A fixed number of independent trials, each with exactly two possible outcomes
• B. Continuous outcomes over an interval
• C. An infinite, unspecified number of trials
• D. Dependent trials only

9. For two mutually exclusive events A and B, P(A∪B) is equal to:

• A. P(A) + P(B)
• B. P(A) · P(B)
• C. P(A) - P(B)
• D. P(A|B)

10. The theorem of total probability is applied when the sample space is partitioned into:

• A. Mutually exclusive and exhaustive events
• B. Independent events only, without any other condition
• C. A single event covering the entire sample space
• D. Continuous intervals only

11. In Bayes' theorem, the probabilities P(Ei), assigned before observing any evidence, are called:

• A. Prior probabilities
• B. Posterior probabilities
• C. Conditional probabilities, without further distinction
• D. Joint probabilities, without further distinction

12. If P(A) = 1 for some event A, then A is said to be a(n):

• A. Certain (sure) event
• B. Impossible event
• C. Mutually exclusive event, without further qualification
• D. Independent event, without further qualification