If two dice are thrown simultaneously,then the probability that $1$ comes on the first die is

Two friends $A$ and $B$ apply for a job in the same company. The probability of $A$ getting selected is $\frac{2}{5}$ and that of $B$ is $\frac{4}{7}$. Then the probability that one of them is selected is:

$A$ mathematics problem is given to three students $A, B$,and $C$. The probabilities of them solving the problem are $1/2, 1/3$,and $1/4$ respectively. What is the probability that the problem is solved?

Let $A$ and $B$ be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that $A$ or $B$ occurs is $\frac{1}{2}$. Then,the probability that both of them occur together is:

Two dice are thrown together. The probability that at least one will show its digit $6$ is

Events $A, B$ and $C$ are mutually exclusive events such that $P(A)=\frac{3x+1}{3}$,$P(B)=\frac{1-x}{4}$ and $P(C)=\frac{1-2x}{2}$. The set of possible values of $x$ is in the interval