Let Ajay will not appear in JEE exam with probability $\mathrm{p}=\frac{2}{7}$, while both Ajay and Vijay will appear in the exam with probability $\mathrm{q}=\frac{1}{5}$. Then the probability, that Ajay will appear in the exam and Vijay will not appear is :

A bag contains $19$ tickets numbered from $1$ to $19$. A ticket is drawn and then another ticket is drawn without replacement. The probability that both the tickets will show even number, is

The probability of obtaining an even prime number on each die, when a pair of dice is rolled is

Two dice are thrown. The events $A,\, B$ and $C$ are as follows:

$A:$ getting an even number on the first die.

$B:$ getting an odd number on the first die.

$C:$ getting the sum of the numbers on the dice $\leq 5$

State true or false $:$ (give reason for your answer)

Statement : $A$ and $B^{\prime }$ are mutually exclusive

Two numbers are selected randomly from the set $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$ without replacement one by one. The probability that minimum of the two numbers is divisible by $3$ or maximum of the two numbers is divisible by $4$ , is