$\begin{array}{1 1}(A)\;\large\frac{1}{4}\\(B)\;\large\frac{1}{2}\\(C)\;\large\frac{1}{3}\\(D)\;\large\frac{1}{7}\end{array} $

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Step 1:

Let the chance of John promotion =x

$\therefore$ P(John)=x

P(Gurpreet)=x

P(Rita)=2x

P(Aslam)=4x

$\therefore$ P(John)+P(Gurpreet)+P(Rita)+P(Aslam)=1

(Sum of all probabilities =1)

$\Rightarrow x+x+2x+4x=1$

$\Rightarrow 8x=1$

$\Rightarrow x=\large\frac{1}{8}$

P(John promoted)=x=$\large\frac{1}{8}$

P(Gurpreet promoted)=x=$\large\frac{1}{8}$

Step 2:

P( John $\cup$ Gurpreet)=P(John)+P(Gurpreet)-P(John $\cap$ Gurpreet)

$\Rightarrow \large\frac{1}{8}+\frac{1}{8}$

P(John $\cap$ Gurpreet)=$\phi$

$\Rightarrow \large\frac{2}{8}$

$\Rightarrow \large\frac{1}{4}$

Hence (A) is the correct answer.

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