HMMT 1999 V9

As part of his effort to take over the world, Edward starts producing his own currency. As part of an effort to stop Edward, Alex works in the mint and produces 1 counterfeit coin for every 99 real ones. Alex isn't very good at this, so none of the counterfeit coins are the right weight. Since the mint is not perfect, each coin is weighed before leaving. If the coin is not the right weight, then it is sent to a lab for testing. The scale is accurate $95 \%$ of the time, $5 \%$ of all the coins minted are sent to the lab, and the lab's test is accurate $90 \%$ of the time. If the lab says a coin is counterfeit, what is the probability that it really is?