CUET Mathematics 2025 14 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 a person A speaks the truth in 80% cases and the person B speaks the truth in 75% cases, then the probability that they contradict each other in a statement is

If A and B are independent events, then which of the following statements are TRUE?

(A) $P(A \cap B) = P(A).P(B)$

(B) $P(A \cap B) = P(A) - P(B)$

(C) $P(A \cup B) = P(A) + P(B) - P(A).P(B)$

(D) $P(A \cap B) = P(A). P(B|A)$

Choose the correct answer from the options given below: