Given Sample Space, S = John promoted, Rita promoted, Aslam promoted, Gurpreet promoted
Let
E1 = events that John promoted
E2 = events that Rita promoted
E3 = events that Aslam promoted
E4 = events that Gurpreet promoted
It is given that chances of John’s promotion is same as that of Gurpreet
P(E1) = P(E4) …(i)
It is given that Rita’s chances of promotion are twice as likely as John
P(E2) = 2P(E1) …(ii)
and Aslam’s chances of promotion are four times that of John
P(E3) = 4P(E1) …(iii)
Since, sum of all probabilities = 1
⇒ P(E1) + P(E2) + P(E3) + P(E4) = 1
⇒ P(E1) + 2P(E1) + 4P(E1) + P(E1) = 1
⇒ 8P(E1) = 1
⇒ P(E1) = 1/8 …(iv)
(a) P (John promoted) = P(E1)
= 1/8 [from (iv)]
P (Rita promoted) = P(E2)
= 2P(E1) [from (ii)]
= 2 x 1/8 [from (iv)]
= 1/4
P (Aslam promoted) = P(E3)
= 4P(E1) [from (iii)]
= 4 x 1/8 [from (iv)]
= 1/2
P (Gurpreet promoted) = P(E4)
= P(E1) [from (i)]
= 1/8
(b) Given A = (John promoted or Gurpreet promoted)
∴, A = E1⋃ E4
P(A) = P(E1⋃ E4)
= P(E1) + P(E4) – P(E1⋂ E4)
[∵ By general addition rule]
= P(E1) + P(E1) – 0 [from (i)]