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Question

Urn A contains 6 red, 4 white balls and urn B contains 4 red and 6 white balls.  One ball is drawn at random from the urn A and placed in the urn B.  Then one ball is drawn at random from the urn B and placed in the urn A.  If one ball is now drawn from the urn A,  the probability that it is found to be red is:


A
3255
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B
3045
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C
3250
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D
150
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Solution

The correct option is C 3255
Case I: Red ball from A to B, red ball from B to A, then red ball from ABBA,Red from A
           (R)     (R)
P1=610×511×610
Case II :  ABBA,R from A
                   (R)      (W)
 P2=610×611×510
Case III : ABBA, R from A
                   (W)         (R)
P3=410×411×710
Case Iv : ABBA, R from A
                  (W)        (W)
P4=410×711×610
Required Probaility =180+180+112+1681100
=6401100=3255

 
 

Mathematics

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