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Bag I contains 3 black and 2 white balls; Bag II contains 2 black and 4 white balls. A bag and a ball are selected at random. Determine the probability of selecting a black ball.

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

  • 1 Answer

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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:

    G i v e n     t h a t                   b a g   I = { 3 B , 2 W } a n d                                             b a g   I I = { 2 B , 4 W } L e t         E 1 = T h e     e v e n t     t h a t     b a g   I     i s     s e l e c t e d                       E 2 = T h e     e v e n t     t h a t     b a g   I I     i s     s e l e c t e d a n d         E = T h e     e v e n t     t h a t     a     b l a c k     b a l l     i s     s e l e c t e d ∴               P ( E 1 ) = 1 2 ,     P ( E 2 ) = 1 2 ,     P ( E / E 1 ) = 3 5     a n d     P ( E / E 2 ) = 1 3 ∴                   P ( E ) = P ( E 1 ) . P ( E / E 1 ) + P ( E 2 ) . P ( E / E 2 )                                                   = 1 2 × 3 5 + 1 2 × 1 3 = 3 1 0 + 1 6 = 9 + 5 3 0 = 1 4 3 0 = 7 1 5 H e n c e ,     t h e     r e q u i r e d     p r o b a b i l i t y     i s     7 1 5 .

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