Two local factories produce microwaves. Each microwave produced at factory A is defective with probability 0.05, while each one produced at factory B is defective with probability 0.01. Suppose you purchase two microwaves that were produced at the same factory, which is equally likely to have been either factory A or factory B. If the first microwave that you check is defective, what is the conditional probability that the other one is also defective?

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