As the title states we need to find $P(D)$ given that $P(C)={9\over20}$, P(C|D')={3\over7} and $P(C|D)={6\over13}$. I have been hitting my head against a brick wall for the past half an hour or so, unable to make much progress.
So far all that I have managed to do is some algebraic manipulation with ${6\over13}={P(C\cap D)\over P(D)}$ and {3\over7}={P(C\cap D')\over P(D')}. However I don't seem to be making any progress. Does anyone have any suggestions on a continuation?