Let's play a game where the contestant has to choose a marble from one of the two given boxes, each of which are full of total ten green and yellow marbles. Now, to choose which box to pick the marble from, the contestant has to roll an unbiased dice. If an odd number shows up, then she chooses the first box, while if an even number comes up, then she chooses the second box. The first box contains 7 green and 3 yellow marbles, while the second box has 4 green and 6 yellow marbles. Given that the contestant picks up a green marble, what is the probability that the second box was chosen?

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