Bag #1

900 red eggs

100 blue eggs

Bag #2

100 red eggs

900 blue eggs

You are given one of these two bags (50/50 chance) randomly.

You perform a set of trials where you take out one egg randomly from your bag, note the color, then put it back in, and repeat.

You drew 8 red eggs and 2 blue eggs from your bag during this trial. What is the probabilty (%) that you have Bag #1?

I thought it was 50% because you could have drawn 8 red and 2 blue from bag #2 as well, since drawing eggs and putting them back does not change the bag's contents...