7 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 \(B\).
- Complete the tree diagram below, giving the remaining four probabilities in terms of \(x\).
\includegraphics[max width=\textwidth, alt={}, center]{217c5a58-2966-4b86-b3b6-9d1676d2979c-12_688_759_484_731} - Show that the probability that both balls chosen are blue is \(\frac { 4 } { x + 10 }\).
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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