Box $P$ has $2$ red balls and $3$ blue balls and box $Q$ has $3$ red balls and $1$ blue ball. A ball is selected as follows: (i) select a box (ii) choose a ball from the selected box such that each ball in the box is equally likely to be chosen. The probabilities of selecting boxes $P$ and $Q$ are $\dfrac{1}{3}$ and $\dfrac{2}{3}$ respectively. Given that a ball selected in the above process is a red ball, the probability that it came from the box $P$ is:
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$\dfrac{4}{19}$
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$\dfrac{5}{19}$
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$\dfrac{2}{9}$
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$\dfrac{19}{30}$
