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An urn contains m white and n black balls. A ball is drawn at random and is put back into the urn along with k additional balls of the same colour as that of the ball drawn. A ball is again drawn at random. Show that the probability of drawing a white ball now does not depend on k .

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

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    Answered by

    alok kumar singh | Contributor-Level 10

    3 months ago

    This is a  Short Answer Type Questions as classified in NCERT Exemplar

    Sol:

    L e t     A     b e     t h e     e v e n t     h a v i n g     m     w h i t e     a n d     n     b l a c k     b a l l s .                   E 1 = { f i r s t     b a l l     d r a w n     o f     w h i t e     c o l o u r }                   E 2 = { f i r s t     b a l l     d r a w n     o f     b l a c k     c o l o u r }                   E 3 = { second  ball  drawn  of  white  colour } P ( E 1 ) = m m + n ,     P ( E 2 ) = n m + n ,     P ( E 3 / E 1 ) = m + k m + n + k ,     P ( E 3 / E 2 ) = m m + n + k N o w ,     P ( E 3 ) = P ( E 1 ) . P ( E 3 / E 1 ) + P ( E 2 ) . P ( E 3 / E 2 )                                                           = m m + n × m + k m + n + k + n m + n × m m + n + k                                                           = m m + n + k [ m + k m + n + n m + n ]                                                             = m m + n + k [ m + n + k m + n ] = m m + n H e n c e ,     t h e     p r o b a b i l i t y     o f     d r a w n i n g     a     w h i t e     b a l l     d o e s     n o t     d e p e n d     u p o n     k .

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