**Solution:**

Given that: Sample Space, S John promoted, Rita promoted, Aslam promoted, Gurpreet promoted

Let’s say

Events that John promoted

Events that Rita promoted

Events that Aslam promoted

Events that Gurpreet promoted

Given that chances of John’s promotion is same as that of Gurpreet

Given that Rita’s chances of promotion are twice as likely as John

and chances of Aslam’s promotion are four times that of John

As, the sum of all probabilities

**(a)** John promoted

from eq.(4)

Rita promoted

From eq. 2 we have

From eq. 4

Aslam promoted

From eq.3 we have

From eq.4 it can be written as

Gurpreet promoted

From eq.1

Gurpreet promoted

From 1

**(b)** It is given that John promoted or Gurpreet promoted)

Using the general rule of addition, we have