In a casino in Liverpool, there are two slot machines: if you play on the first one (machine A), you win 10% of the time. If you play on the second one (machine B), you win 20% of the time. You do not know which machine is which.

Your strategy: you assume the machines have an equal chance of being the better one, you select one of the two at random and put a coin in it. You lose the first bet. What is the probability that you selected machine B?