In an effort to curry favor with the course staff, Jared decides to buy some baked goods to bring to the next staff meeting. He purchases three boxes of baked goods. The first box contains 1 donut and 2 brownies, the second contains 4 donuts and 2 brownies, and the third contains 2 donuts and six brownies. However, on his way to the staff meeting, Jared gets hungry, and he uniformly at random selects 1 baked good from each box to eat. What is the probability that he ate a donut from the first box, given that exactly 2 of the baked goods he ate were donuts?