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Four candidates   A , B , C , D have applied for the assignment to coach a school cricket team. If   A is twice as likely to be selected as B , and   B and   C are given about the same chance of being selected, while C  is twice as likely to be selected as D , what are the probabilities that:

(a) C will be selected?

(b) A will not be selected?

0 4 Views | Posted 3 months ago
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    Answered by

    Payal Gupta | Contributor-Level 10

    3 months ago

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

    G i v e n     t h a t     A     i s     t w i c e     a s     l i k e l y     t o     b e     s e l e c t e d     a s     B i . e . ,                                                             P ( A ) = 2 P ( B ) a n d     C     i s     t w i c e     a s     l i k e l y     t o     b e     s e l e c t e d     a s     D ∴                                                                     P ( C ) = 2 P ( D )                     ⇒ P ( B ) = 2 P ( D ) ⇒                                                               P ( A ) 2 = 2 P ( D )                     ⇒ P ( D ) = 1 4 P ( A ) N o w     B     a n d     C     a r e     g i v e n     a b o u t     t h e     s a m e     c h a n c e ∴                                                                     P ( B ) = P ( C ) Since,          sum  of  all  probabilities=1 ∴                         P ( A ) + P ( B ) + P ( C ) + P ( D ) = 1 ⇒               P ( A ) + P ( A ) 2 + P ( A ) 2 + P ( A ) 4 = 1 ⇒ 4 P ( A ) + 2 P ( A ) + 2 P ( A ) + P ( A ) = 4 ⇒                                                                                                                   9 P ( A ) = 4           ⇒ P ( A ) = 4 9 ( a )       P ( C     w i l l     b e     s e l e c t e d ) = P ( C ) = P ( B ) = P ( A ) 2                                                                                                                 = 4 9 × 1 2 = 2 9 ( b ) P ( A     w i l l     n o t     b e     s e l e c t e d ) = P ( A ' ) = 1 − P ( A )                                                                                                   &thi

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