Conditional probability with an uncertain conditional event

#2
You lost me here: "consider that A = red jar and B = black ball, so that the probability tree is telling us that 80% of the jars are red, and that 10% of the balls in the red jars are black, and that 90% of the balls in the other jars are black."

Are your events defined properly? I am confused. Is this just a hypothetical example that you made up? Perhaps it's this mismatch color example that's turning people around?
 
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#3
Hmm. I don't see an issue, but I can appreciate how that sentence might be confusing. What if I expanded it to say the following:
"To see how this could apply to our example tree consider that we're using the classic example of drawing balls from jars. A is the "red jar" event, so that the probability tree is telling us that if we randomly select a jar to draw a ball from, there is an 80% chance of drawing from a red jar and a 20% chance of drawing from a non-red jar. B is the "black ball" event, so that the probability tree is telling us that if we draw from a red jar, there is a 10% chance that the ball will be black (and thus a 90% chance that it will be something other than black) and if we draw from a non-red jar, there is a 90% chance that the ball will be black (and thus a 10% chance that it will be something other than black)."