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  • 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

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).

Answers (1)

Given:

Sample Space (S) = John promoted, Rita promoted, Aslam promoted, Gurpreet promoted

Chances of John’s promotion is same as Gurpreet’s, P (E1) = P (E4)

Rita’s chances of promotion as twice as john’s, P (E2) = 2 P(E1)

& chances of Aslam’s promotion are four times that of John’s, P (E3) = 4 P(E­1)

Now, let us consider that,

E1 → events that John promoted

E2 → events that Rita promoted

E3 → events that Aslam promoted

E4 → events that Gurpreet promoted

Now, we know that,

Sum of all probabilities = 1

Thus, P(E1) + P(E2) + P(E3) + P(E4) = 1

P(E1) + 2 P(E1) + 4 P(E1) + P(E1) = 1

8 P(E1) = 1

P (E1) = 1/8

Now,

  1. P (John promoted) = P (E1) = 1/8

P (Rita promoted) = P (E2) = 2P (E1)

                                    = 2 x 1/8

                                    = 1/4

P (Aslam promoted) = P (E3) = 4P (E1)

                                          = 4 x 1/8

                                          = 1/2

       P (Gurpreet promoted) = P (E4) = P (E1)

                                          = 1/8

  1. A = John or Gurpreet promoted     …….. (Given)

Thus, A = E1 U E2

P (A) = P (E1 U E2)

            = P (E1) + P (E4) – P (E1 ∩ E2)       ……. (general addition rule)

            = P (E1) + P (E1) – 0

            = 1/8 + 1/8

            = 2/8

            = 1/4

Posted by

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