[latex]
\[
\textbf{MCQs on Probability Theory with Answers}
\]
\[
\textbf{Q1: The probability of an impossible event is:}
\]
\[
\text{(A) } 0 \quad
\text{(B) } 1 \quad
\text{(C) } Between 0 and 1 \quad
\text{(D) } None of these
\]
\[
\textbf{Answer: (A) } 0
\]
\[
\textbf{Q2: The sum of probabilities of all possible outcomes of an experiment is:}
\]
\[
\text{(A) } 0 \quad
\text{(B) } 1 \quad
\text{(C) } Greater than 1 \quad
\text{(D) } None of these
\]
\[
\textbf{Answer: (B) } 1
\]
\[
\textbf{Q3: Two events are independent if:}
\]
\[
\text{(A) } Their probabilities are equal \quad
\text{(B) } The occurrence of one does not affect the other \quad
\text{(C) } They cannot occur together \quad
\text{(D) } None of these
\]
\[
\textbf{Answer: (B) } The occurrence of one does not affect the other
\]
\[
\textbf{Q4: The conditional probability of an event A given event B is defined as:}
\]
\[
\text{(A) } P(A \cap B) / P(B) \quad
\text{(B) } P(A) + P(B) \quad
\text{(C) } P(A \cup B) / P(B) \quad
\text{(D) } None of these
\]
\[
\textbf{Answer: (A) } P(A \cap B) / P(B)
\]
\[
\textbf{Q5: A random experiment is:}
\]
\[
\text{(A) } An experiment with a predictable outcome \quad
\text{(B) } An experiment with uncertain outcomes \quad
\text{(C) } An experiment that cannot be repeated \quad
\text{(D) } None of these
\]
\[
\textbf{Answer: (B) } An experiment with uncertain outcomes
\]
\[
\textbf{Q6: If two events A and B are mutually exclusive, then:}
\]
\[
\text{(A) } P(A \cap B) = P(A) + P(B) \quad
\text{(B) } P(A \cap B) = 0 \quad
\text{(C) } P(A \cup B) = 0 \quad
\text{(D) } None of these
\]
\[
\textbf{Answer: (B) } P(A \cap B) = 0
\]
\[
\textbf{Q7: The expected value of a random variable X is:}
\]
\[
\text{(A) } The sum of all possible values of X \quad
\text{(B) } The weighted average of all possible values of X \quad
\text{(C) } Always equal to zero \quad
\text{(D) } None of these
\]
\[
\textbf{Answer: (B) } The weighted average of all possible values of X
\]
\[
\textbf{Q8: The probability density function (PDF) is used for:}
\]
\[
\text{(A) } Discrete random variables \quad
\text{(B) } Continuous random variables \quad
\text{(C) } Both discrete and continuous variables \quad
\text{(D) } None of these
\]
\[
\textbf{Answer: (B) } Continuous random variables
\]
\[
\textbf{Q9: Bayes’ theorem relates:}
\]
\[
\text{(A) } Prior and posterior probabilities \quad
\text{(B) } Mutually exclusive events \quad
\text{(C) } Independent events \quad
\text{(D) } None of these
\]
\[
\textbf{Answer: (A) } Prior and posterior probabilities
\]
\[
\textbf{Q10: The variance of a random variable X measures:}
\]
\[
\text{(A) } The central tendency of X \quad
\text{(B) } The spread or dispersion of X \quad
\text{(C) } The mode of X \quad
\text{(D) } None of these
\]
\[
\textbf{Answer: (B) } The spread or dispersion of X
\]