If $A, B, C$ are three mutually exclusive and exhaustive events of an experiment such that $P(A)=2 P(B)=3 P(C)$,then $P(B)$ is equal to

If a point $A(x, y)$ lies in the region bounded by the $y$-axis,straight lines $2y+x=6$ and $5x-6y=30$,then the probability that $y < 1$ is

If the events $A$ and $B$ are mutually exclusive events such that $P(A) = \frac{3x + 1}{3}$ and $P(B) = \frac{1 - x}{4}$,then the set of possible values of $x$ lies in the interval

$A$ problem in Algebra is given to two students $A$ and $B$ whose chances of solving it are $\frac{2}{5}$ and $\frac{3}{4}$ respectively. The probability that the problem is solved if both of them try independently is

Two dice are rolled one after the other. The probability that the number on the first die is smaller than the number on the second die is

The probabilities of $A, B,$ and $C$ solving a problem are $\frac{1}{3}, \frac{2}{7},$ and $\frac{3}{8}$ respectively. If all three try to solve the problem simultaneously,the probability that exactly one of them will solve it is: