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

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