To clarify (in case unclear):

"If a green ball or a red ball is drawn on 1st draw,

then the ball is put back in the bag; but not if blue."

The ball that is put back counts as 1st draw;

like, it doesn't mean "start over"; example:

G is drawn; then put back so we have [G R B B] for 2nd draw;

possible to draw G again, so end up with having drawn 2 G's.

And on this:

"What is the probability of ending up with a pair

containing 1 blue and 1 green ball, or 1 blue and 1 red ball?

Really means: what is probability that the 2 balls

drawn are B and G or B and R (order unimportant)

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We're all here because we're not all there!