0
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ 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
1
$\begingroup$

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).

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.