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 promoted, 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 Johns. Aslam’s chances are four times that of John.
(a) Determine P (John promoted)
P (Rita promoted)
P (Aslam promoted)
P (Gurpreet promoted)
(b) If A = {John promoted or Gurpreet promoted}, find P (A).
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 promoted, 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 Johns. Aslam’s chances are four times that of John.
(a) Determine P (John promoted)
P (Rita promoted)
P (Aslam promoted)
P (Gurpreet promoted)
(b) If A = {John promoted or Gurpreet promoted}, find P (A).

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