Classical probability

If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is :

Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements, is :

Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is

The probability that $x_1+x_2+x_3$ is odd, is

The probability that $x_1$, $x_2$, $x_3$ are in an arithmetic progression, is

Let A and B be two events such that $P\left(\overline{A\cup B}\right)=\dfrac16$, $P(A\cap B)=\dfrac14$ and $P\left(\bar A\right)=\dfrac14$, where $\bar A$ stands for the complement of the event A. Then the events A and B are :

If A and B are two events such that $P(A\cup B)=P(A\cap B)$, then the incorrect statement amongst the following statements is :

A set S contains 7 elements. A non-empty subset A of S and an element $x$ of S are chosen at random. Then the probability that $x\in A$ is :

A number $x$ is chosen at random from the set {1, 2, 3, 4, ....., 100}. Define the event : A = the chosen number $x$ satisfies
$$\frac{(x-10)(x-50)}{(x-30)}\ge0$$
Then P(A) is :

Four fair dice $D_1$, $D_2$, $D_3$ and $D_4$, each having six faces numbered 1, 2, 3, 4, 5 and 6, are rolled simultaneously. The probability that $D_4$ shows a number appearing on one of $D_1$, $D_2$ and $D_3$ is

The probability of the drawn ball from $U_2$ being white is

Let $\omega$ be a complex cube root of unity with $\omega\ne1$. A fair die is thrown three times. If $r_1$, $r_2$ and $r_3$ are the numbers obtained on the die, then the probability that $\omega^{r_1}+\omega^{r_2}+\omega^{r_3}=0$ is

Consider the system of equations $ax+by=0$, $cx+dy=0$, where $a,b,c,d\in\{0,1\}$.

STATEMENT-1: The probability that the system of equations has a unique solution is $\dfrac38$.

and

STATEMENT-2: The probability that the system of equations has a solution is 1.