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And the answer is,
the prior isn't affected by the measurement,
so the probability of 0 is at red,
and the probability of 1 at green,
despite the fact that it's all red.
To see this, you find the joint of seeing it red and seeing red
is 0 times 0.8, that's 0.
That's the same join for green is
1 times 0.2.
So you have to normalize 0 and 0.2.
The sum of those is 0.2.
So let's divide 0 by 0.2, gives us 0,
and 0.2 divided by 0.2 gives us 1.
These are exactly the numbers over here.