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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 from the urn A and placed in the urn B. Then one ball is drawn at random from urn B and placed in the urn A. if one ball is now drawn from the urn A, then the probability that it is found to be red is

A
3255
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B
3040
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C
3250
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D
34
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Solution

The correct option is A 3255

case(i): red ball from A to B, red ball from B to A ,then red ball from A
P1=610×511×610
Case(ii): red ball from A to B, white ball from B to A, red ball from A
P2=610×611×510
Case(iii): white ball from A to B, red ball from B to A, red ball from A
P3=410×411×710
Case(iv): white ball from A to B, white ball from B to A, red ball from A
P4=410×711×610
Therefore required probability =P1+P2+P3+P4=6401100=3255

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