An integer $x$ is chosen at random from $1$ to $50$. The probability that $x + \frac{336}{x} \leq 50$ is

If $A, B$ and $C$ are mutually exclusive and exhaustive events of a random experiment such that $P(A) = \frac{2}{3} P(B)$ and $P(B) = 2 P(C)$,then $P(A \cup C) =$

$A$ die is thrown. Find the probability of the following event: $A$ number less than $6$ will appear.

$A$ problem is given to $3$ students $A, B$ and $C$ whose chances of solving it are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. Then,the probability of the problem being solved by exactly one of them,if all the three try independently,is

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three persons apply for the same house is

One die of red colour,one of white colour and one of blue colour are placed in a bag. One die is selected at random and rolled,its colour and the number on its uppermost face is noted. Describe the sample space.