CUET Mathematics 2025 14 May Shift 1 PYQs

Let A and B be two events. Then which of the following statements are TRUE?

(A) $P(\overline{B}|A) = \frac{P(A \cap B)}{P(A)}$, provided $P(A) \neq 0$

(B) $P(B') = 1 + P(B)$

(C) $P(A \cup B) = P(A) + P(B) + P(A \cap B)$

(D) $P(A \cap B) = P(A).P(B)$ If A and B are independent events

Choose the correct answer from the options given below:

A random variable X has the following probability distribution:

X	0	1	2
P(X)	1/4	1/2	1/4

then, which of the following is correct?

If the binomial distribution $X\sim B(n, p)$ of mean 3 and variance $\frac{3}{2}$ $(p + q) = 1$, then which of the following is/are TRUE?

(A) $q = \frac{1}{2}$, $n = 6$

(B) $P(X \leq 5) = \frac{63}{64}$, $p = \frac{1}{2}$

(C) $q = \frac{1}{3}$, $p = \frac{2}{3}$

(D) $P(X = 4) = \frac{15}{64}$, $n = 6$

Choose the correct answer from the options given below: