Hi I really need help with this too! I cannot see where I went wrong, really. Thank you so much in advance! Really need this!
! I've attached the question itself and my attempt to find P(D) to which I failed.
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It is hard to read your images.
$\displaystyle \begin{align*} \mathcal{P}(C) &= \mathcal{P}(C\cap D)+ \mathcal{P}(C\cap D') \\\frac{9}{20}&=\frac{6}{13}\mathcal{P}(D)+\frac{3 }{7}(1-\mathcal{P}(D))\end{align*}$
Solve for $\displaystyle \mathcal{P}(D).$
Thank you so much!
I didn't know that P(C|D)+P(C|D') = P(C)!
If I expand it out eg. P(C|D)P(D) = P(CnD), it will be quite different from P(C|D')P(D') = P(CnD') so I dont think that's the proof..
Could you teach me how to prove P(C|D)+P(C|D') = P(C) using any method or even the venn diagram?