Two distinct numbers $a$ and $b$ are selected at random from $1,2,3, \ldots, 50$. The probability, that their product $a b$ is divisible by 3 , is

If a random variable $x$ has the probability distribution

$$ \begin{array}{|c|c|c|c|c|c|c|c|c|} \hline x & 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline \mathrm{P}(x) & 0 & 2 \mathrm{k} & \mathrm{k} & 3 \mathrm{k} & 2 \mathrm{k}^2 & 2 \mathrm{k} & \mathrm{k}^2+\mathrm{k} & 7 \mathrm{k}^2 \\ \hline \end{array} $$

$$ \text { then } \mathrm{P}(3 < x \leq 6) \text { is equal to } $$

Let the mean and variance of 7 observations $2,4,10, x, 12,14, y, x>y$, be 8 and 16 respectively. Two numbers are chosen from $\{1,2,3, x-4, y, 5\}$ one after another without replacement, then the probability, that the smaller number among the two chosen numbers is less than 4 , is :

If A and B are two events such that $P(A) = 0.7$, $P(B) = 0.4$ and $P(A \cap \overline{B}) = 0.5$, where $\overline{B}$ denotes the complement of B, then $P\left(B \mid (A \cup \overline{B})\right)$ is equal to