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The probability of picking a green jelly bean with the first pick is 4/14 = 2/7, because there are 14 jelly bean in total (6 red + 4 green + 4 blue) and 4 of them are green.
If you pick a green jelly bean at the beginning, you have 13 jelly beans remaining, of which 6 are red. So, the probability of picking a red jelly bean is now 6/13.
You want these two events to happen one after the other, to be more precise you want to pick a green jelly bean with the first pick AND a red jelly bean with the second pick. We know the probabilities of the two events, so we have to multiply them to get the probability of them happening both: