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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 the chances of John’s promotion are the 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.

(a) Determine P (John promoted),

P (Rita promoted),

P (Aslam promoted), and

P (Gurpreet promoted).

(b) If A = {John promoted or Gurpreet promoted}, find P(A).

0 2 Views | Posted 3 months ago
Asked by Shiksha User

  • 1 Answer

  • P

    Answered by

    Payal Gupta | Contributor-Level 10

    3 months ago

    This is a short answer type question as classified in NCERT Exemplar

    L e t     E 1 , E 2 , E 3     a n d     E 4     b e     t h e     e v e n t s     t h a t     J o h n     p r o m o t e d ,     R i t a     p r o m o t e d ,     A s l a m     p r o m o t e d a n d     G u r p r e e t     p r o m o t e d     r e s p e c t i v e l y . ∴     S a m p l e     s p a c e     S = { E 1 , E 2 , E 3 , E 4 } G i v e n     t h a t     p r o b a b i l i t y     o f     J o h n ' s     p r o m o t i o n     i s     s a m e     a s     t h a t     o f     G u r p r e e t ∴                                                   P ( E 1 ) = P ( E 4 ) R i t a ' s     c h a n c e s     o f     p r o m o t i o n     a r e     t w i c e     a s     l i k e l y     a s     J o h n ∴                                                   P ( E 2 ) = 2 P ( E 1 ) A n d     A s l a m ' s     c h a n c e s     o f     p r o m o t i o n     a r e     4     t i m e s     t h a t     o f     J o h n ∴                                                   P ( E 3 ) = 4 P ( E 1 ) Since,  the  sum  of  all  probabilities=1 ∴                 P ( E 1 ) + P ( E 2 ) + P ( E 3 ) + P ( E 4 ) = 1 ⇒ P ( E 1 ) + 2 P ( E 1 ) + 4 P ( E 1 ) + P ( E 1 ) = 1 ⇒                                                                                                                       8 P ( E 1 ) = 1 ⇒                                                                                                                             P ( E 1 ) = 1 8 ( a )     P ( J o h n     p r o m o t e d ) = P ( E 1 ) = 1 8                   P ( R i t a     p r o m o t e d ) = P ( E 2 ) = 2 P ( E 1 ) = 2 × 1 8 = 2 8           P ( A s l a m     p r o m o t e d ) = P ( E 3 ) = 4 P ( E 1 ) = 4 × 1 8 = 4 8 = 1 2 P ( G u r p r e e t     p r o m o t e d ) = P ( E 4 ) = P ( E 1 ) = 1 8 ( b ) P ( J o h n     p r o m o t e d     o r     G u r p r e e t     p r o m o t e d ) = P ( E 1 ∪ E 4 ) ⇒                       &th

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