CUET Mathematics 2025 29 May Shift 2 PYQs

Which of the following statements are correct?

(A) If E and F are independent events then $P(E \cap F) = P(E) \cdot P(F)$

(B) If E and F are mutually exclusive events, then $P(E \cup F) = P(E) + P(F) - P(E) \cdot P(F)$

(C) The conditional probability of an event E, given the occurrence of the event F is given by $\frac{P(E \cap F)}{P(F)}, P(F) \neq 0$

(D) If E and F be the events associated with the sample space S of an experiment, then $P(\overline{E}|F) = 2 - P(E|F)$

Choose the correct answer from the options given below:

If X is a random variable and $a$, $b$ are real numbers, then which of the following statements are true?

(A) $Var(aX+b) = a^2 Var(X)$

(B) $E(aX+b)= a E(X) + b$

(C) $E(aX+b)= a E(X) - E(b)$

(D) $Var(aX+b)= a Var(X) + b$

Choose the correct answer from the options given below:

A letter is known to have come either from KOLKATA or TATANAGAR. On the envelope just two consecutive letters TA are visible. The probability that letter has come from TATANAGAR is