Finding P(D) given 3 equations

[dxoo]

Given:
[MATH] P(C) = 3/7\\ P(D|C') = 2/5\\ P(D'|C) = 3/4\\ [/MATH]
How would I find the probability of even D occurring?

I've tried writing the given equations differently but I got stuck finding D intersect C'.
Any help is appreciated.

 

[pka]

Given:[MATH]P(C) = 3/7\\ P(D|C') = 2/5\\ P(D'|C) = 3/4\\[/MATH]How would I find the probability of even D occurring?

\(\mathcal{P}(D|C')=\dfrac{\mathcal{P}(D\cap C')}{\mathcal{P}(C')}\) then \(\mathcal{P}(D\cap C')=\dfrac{4}{7}\cdot\dfrac{2}{5}=\dfrac{8}{35}\)
Use that as a model and finish it off.

HINT: \(\mathcal{P}(D\cap C)=\mathcal{P}(C)-\mathcal{P}(D'\cap C)\)