Let Ajay will not appear in JEE exam with probability p = 2 7 , while both Ajay and Vijay will appear in the…

The probability that Ajay will not appear in exam is, $P\left(A^{\text{'}}\right)=p=\frac{2}{7}$.

$\Rightarrow P\left(A\right)=\frac{5}{7}$

The probability that Ajay and Vijay will appear in exam is, $P\left(A\cap V\right)=q=\frac{1}{5}$.

$\Rightarrow P\left(A\right)\times P\left(V\right)=\frac{1}{5}$

$\Rightarrow P\left(V\right)=\frac{1}{5}\times \frac{7}{5}$

$\Rightarrow P\left(V\right)=\frac{7}{25}$

The probability that Ajay will appear and Vijay will not appear in the exam is,

$\Rightarrow P\left(A\cap V^{\text{'}}\right)=\frac{5}{7}\times \frac{18}{25}$

$\Rightarrow P\left(A\cap V^{\text{'}}\right)=\frac{18}{35}$