# One of the four persons John,Rita,Aslam or Gurpreet will be promoted next month.Consequently the sample space consists of four elementary outcomes S={John promoted,Rita promoted,Aslam promted,Gurpreet promoted}.You are told that the chances of John's promotion is same as that of Gurpreet,Rita's chances of promotion are twice as likely as John's,Aslam's chances are four times that of John.If A ={John promoted or Gurpreer promoted} find P(A)

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

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.