Two boxes contain 20 light bulbs each. The material used for the bulbs in one of the two boxes was faulty so that one out of four bulbs go off as soon as you use them. The other box doesn't contain any fault bulbs. One box is selected at random and two bulbs are selected (without replacement) from it and tested. None of these two bulbs go off. What is the probability they are from the box containing the bulbs made from the faulty material?
P(B1) = 0.5 P(B2) = 0.5 P(F | B1) = 0.25 P(F | B2) = 0 P(F^C | B1) = 0.75 P(F^C | B2) = 1
So far I used Bayes' theorem :
P(B1 | F^C) = (P(B1)*(P(F^C | B1)) / ( P(B1)*P(F^C | B1) + P(B2)*P(F^C | B2) ) (0.5*0.75) / ((0.5*0.75)+(0.5*1)) = 3/7
However this is only selecting one bulb, I don't know how to then select bulb two as the box has already been chosen?