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 :

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

The probabilities of winning the race by two athletes $A$ and $B$ are $\frac{1}{5}$ and $\frac{1}{4}.$ The probability of winning by neither of them, is

A bag contains $9$ discs of which $4$ are red, $3$ are blue and $2$ are yellow. The discs are similar in shape and size. A disc is drawn at random from the bag. Calculate the probability that it will be red.

$A$ and $B$ toss a coin alternatively, the first to show a head being the winner. If $A$ starts the game, the chance of his winning is