$\begin{array}{1 1}(A)\;\large\frac{1}{8},\frac{1}{4},\frac{1}{2},\frac{1}{8}\\(B)\;\large\frac{1}{7},\frac{1}{5},\frac{1}{4},\frac{1}{7}\\(C)\;\large\frac{1}{5},\frac{1}{6},\frac{1}{9},\frac{1}{5}\\(D)\;\text{None of these}\end{array} $

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)

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

$\Rightarrow 8x=1$

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

Step 2:

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

P(Rita promoted)=2x=$2\times\large\frac{1}{8}=\frac{1}{4}$

P(Aslam promoted)=4x=$4\times\large\frac{1}{8}=\frac{1}{2}$

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

Hence (A) is the correct answer.

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