We have two boxes box A containing one black and two white m

We have two boxes, box A containing one black and two white marbles, and box B containing three black and two white marbles. One box is selected at random and a marble is drawn at random from the chosen box. Suppose the selected marble is black, what is the chance that the chosen box is B? Suppose t hat 30 percent of the bottles produced in a certain plant are defective. If a bottle is defective, the probability is 0.9 that an inspector will notice it and remove it from the filling line. If a bottle is not defective, the probability is 0.2 that the inspector will think it is defective and remove it from the filling line. If a bottle is removed from the filling line, what is the probability that it is defective?

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