So I have the following problem. There are 300 million people and 2 million of them are green. Say there are 10 people who are terrorists. 9 out of 10 of these terrorists are green.
What is the probability that a random selected green person is a terrorist?
My reasoning:
$P(Green|Terrorist)=9/10$
$P(green)=2/300$
$P(notgreen)=298/300$
$P(not green|Terrorist)=1/10$
So I have almost everything, except $P(green| not terrorist)$. I am not sure how to find this... I was thinking that perhaps it is (2 million-9)/(300 million-10) is this correct? My book states otherwise, it claims it is 2/300 ...
I would appreciate any help
\begin{array}{|c|c|c|c|} \hline 0 & terrorist & no terrorist & total \\ \hline green & 9& 1.999.991&2.000.000 \\ \hline nogreen &1&297.999.999& 298.000.000\\ \hline total &10&299.999.990&300.000.000 \\ \hline \end{array}
Does this table help?