# Calculating conditional probability with tree diagram

Given this tree diagram: (rather poor quality sorry)

How can I find $$P[R|G']$$? I'm really struggling with this question and only managed to find $$P(G) = 0.2327$$ from dividing $$74$$ by the total of $$G + NG = 318$$. I apologize if the context of this question is crucial in finding this problem, if so please comment on that.

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• What do you mean, exactly, by $G'$, as opposed to $G$ ? Is it the same as $NG$ ? – Matti P. Aug 14 at 8:03
• The complement of G which is found by 1 - 0.2327 = 0.7673. – Jeze628 Aug 14 at 8:04
• Main problem is I'm not sure how to find P(R) from that tree diagram alone. – Jeze628 Aug 14 at 8:05
• P(R|NG) is just 0.29, isn't it? – Matthew Daly Aug 14 at 8:07
• Right, I got confused by the figures of G and NG. – Jeze628 Aug 14 at 8:12

Assuming that both $$G'$$ and $$NG$$ both mean the complement of $$G$$, your diagram seems to contain the answer: $$P(R|G')=.29.$$ If you also need the probability of $$R$$ it is $$P(R) =P(R|G)\times P(G) + P(R|G')\times P(G') =.42\times {74\over 74+244} + .29\times {244\over 74+244} =.320252$$ (assuming this is the correct way of getting $$P(G)$$ from your notation).