If $A$ and $B$ are two independent events such that $P(\bar{A})=0.75$,$P(A \cup B)=0.65$ and $P(B)=x$,then find the value of $x$.

Consider the following statements:
Assertion $(A)$: If $P_1, P_2, P_3$ are probabilities of occurrence of three independent events, then the probability of occurrence of at least one of them is $1 - [(1 - P_1)(1 - P_2)(1 - P_3)]$.
Reason $(R)$: For any three independent events $A, B$, and $C$, $P(A \cup B \cup C) = P(A) + P(B) + P(C) - P(A)P(B) - P(A)P(C) - P(B)P(C) + P(A)P(B)P(C)$.
The correct option among the following is:

Ravi and Rashmi each hold $2$ red cards and $2$ black cards (all four red and all four black cards are identical). Ravi picks a card at random from Rashmi and then Rashmi picks a card at random from Ravi. This process is repeated a second time. Let $p$ be the probability that both have all $4$ cards of the same colour. Then,$p$ satisfies

If $A, B$ and $C$ are three independent events of a random experiment such that $P(A \cap B^{c} \cap C^{c}) = \frac{1}{4}$,$P(A^{c} \cap B \cap C^{c}) = \frac{1}{8}$ and $P(A^{c} \cap B^{c} \cap C^{c}) = \frac{1}{4}$,then $P(A), P(B)$ and $P(C)$ are respectively

Two players,$P_1$ and $P_2$,play a game against each other. In every round,each player rolls a fair die once. Let $x$ and $y$ denote the outcomes for $P_1$ and $P_2$. If $x > y$,$P_1$ scores $5$ points and $P_2$ scores $0$. If $x = y$,each scores $2$ points. If $x < y$,$P_1$ scores $0$ and $P_2$ scores $5$. Let $X_n$ and $Y_n$ be the total scores of $P_1$ and $P_2$ after $n$ rounds. Match the following:

List-$I$	List-$II$
$(I)$ Probability of $(X_2 \geq Y_2)$ is	$(P)$ $\frac{3}{8}$
$(II)$ Probability of $(X_2 > Y_2)$ is	$(Q)$ $\frac{11}{16}$
$(III)$ Probability of $(X_3 = Y_3)$ is	$(R)$ $\frac{5}{16}$
$(IV)$ Probability of $(X_3 > Y_3)$ is	$(S)$ $\frac{355}{864}$
	$(T)$ $\frac{77}{432}$

If the probabilities of three independent events occurring are $p_1, p_2, p_3$,what is the probability that at least one of these events occurs?