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There are two bags. The first bag contains 5 white and 3 black balls and the second bag contains 3 white and 5 black balls. Two balls are drawn at ran

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There are two bags. The first bag contains 5 white and 3 black balls and the second bag contains 3 white and 5 black balls. Two balls are drawn at random from the first bag and are put into the second bag without noticing their colours. Then two balls are drawn from the second bag. Find the probability that the balls are white and black. Select the correct answer from above options

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P(W&B)=P1+P2+P3 as they are mutually exclusive P1= .3C2 .8C2 ⋅ .3C1.7C1 .10C2 P2= .3C1.5C1 .8C2 ⋅ .4C1.6C1 .10C2 P3= .5C2 .8C2 .5C1.5C1 .10C2 So,P(W&B)= .3C2 .8C2 ⋅ .3C1.7C1 .10C2 + .3C1.5C1 .8C2 ⋅ .4C1.6C1 .10C2 + .5C2 .8C2 .5C1.5C1 .10C2

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