Given this tree diagram: (rather poor quality sorry) enter image description here

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.

  • $\begingroup$ What do you mean, exactly, by $G'$, as opposed to $G$ ? Is it the same as $NG$ ? $\endgroup$ – Matti P. Aug 14 at 8:03
  • $\begingroup$ The complement of G which is found by 1 - 0.2327 = 0.7673. $\endgroup$ – Jeze628 Aug 14 at 8:04
  • $\begingroup$ Main problem is I'm not sure how to find P(R) from that tree diagram alone. $\endgroup$ – Jeze628 Aug 14 at 8:05
  • 2
    $\begingroup$ P(R|NG) is just 0.29, isn't it? $\endgroup$ – Matthew Daly Aug 14 at 8:07
  • $\begingroup$ Right, I got confused by the figures of G and NG. $\endgroup$ – 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).


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