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navi

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There are 5 history courses of interest to Howard, including 3 in the afternoon, and there are 6 psychology courses, including 4 in the afternoon. Howard picks a course by selecting a dept at random, then selecting a course at random. Find the pr that the course he selects is in the afternoon.

The answer is 19/30, but I get 13/30 by doing this:

For the history dept, the probability of an afternoon class is 1/2 x 3/5, or 3/10, and for the psych dept, the pr of an afternoon class is 1/2 x 4/6, or 1/3. I then add 1/3 and 3/10 and I get 13/30, but that is not the answer and I have no idea what I could be doing wrong...

Please help :(