Box $$\(A\)$$ contains 6 red balls and 4 blue balls. Box $$\(B\)$$ contains $$\(x\)$$ red balls and 9 blue balls. A ball is chosen at random from box $$\(A\)$$ and placed in box $$\(B\)$$. A ball is then chosen at random from box $$\(B\)$$. It is given that the probability that both balls chosen are blue is $$\(\frac{1}{6}\)$$. Find the probability, correct to 3 significant figures, that the ball chosen from box $$\(A\)$$ is red given that the ball chosen from box $$\(B\)$$ is red. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

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