Once of the four persons John, Rita, Aslam or Gurpreet will be promoted next month. Consequently the sample space consists of four elementary outocomes 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 John's Aslam's chances are four times that of John.
(i) Determine
P (John promoted),
P (Rita promoted),
P (Aslam promoted),
P (Gurpreet promoted).
If A= {John promoted or Gurpreet promoted}, find P (A)

Explanation

Let `E_(1)` = John promoted
`E_(2)`=Rita promoted
`E_(3)`=Aslam promoted
`E_(4)`=Gurpreet promoted
Given, sample space, s= {John promoted, Rits promoted, Aslam promoted, Gurpreet promoted}.
`i.e.," "S={E_(1),E_(2),E_(3),E_(4)}`
It is given that, chances of John's promotion is same as that of Gurpreet.
`P(E_(1))=P(E_(4))`
Rita's chances of promotion are twice as likely as John.
`P(E_(2))=2P(E_(1))`
And Aslam's chance of promotion are four times that of John.
`P(E_(3))=4P(E_(1))`
`"Now" " "P(E_(1))+P(E_(2))+P(E_(3))+P(E_(4))=1`
`rArr " "P(E_(1))+2P(E_(1))+4P(E_(1))+P(E_(1))=1`
`rArr " "8P(E_(1))=1`
`therefore " "P(E_(1))=(1)/(8)`
(i) `"P(John promoted)"=P(E_(1))=(1)/(8)`
`"P(Rita promoted)"=P(E_(2))=2P(E_(1))=2xx(1)/(8)=(2)/(8)=(1)/(4)`
`"P(Aslam promoted)"=P(E_(3))=4P(E_(1))=4xx(1)/(8)=(1)/(2)`
`"P(Gurpreet promoted)"=P(E_(4))=P(E_(1))=(1)/(8)`
(ii) `"A=John promoted or Gurpreet promoted " A=E_(1)cupE_(4)`
`P(A)=P(E_(1)cupE_(4))=P(E_(1))+P(E_(4))-P(E_(1)capE_(4))`
`=(1)/(8)+(1)/(8)-0 " "[becauseP(E_(1)capE_(4))=0]`
`=(2)/(8)=(1)/(4)`