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If you draw a Venn diagram, you'll have 2 overlapping circles where the first circle is labeled Honor Roll Students and the other is School Paper.
Since "There are 38 student council members who are on the honor roll and 5 that write for the schol paper", this means that in the first circle alone (ignore the other circle for now), there are 38 students. For the other circle, there are 5 students (ignoring the first circle).
Now because some of the 38 students who are on the honor roll could also be in the school paper, this means that we have some overlap. Let's call the number of overlapping students "x"
So when we say that "29 are either on the honor roll or write for the school paper.", we are saying that there are 29 kids who are on the honor roll OR on the school paper (and not both). So we must subtract out the overlapping amount like this:
So there are 14 people on both. So the probability is:
P(both) = # in both / total = 14/50 = 7/25
which gives the answer of B)