Conditional defectives from a random factory

Two factories $F_1$ and $F_2$ produce cricket bats that are labelled. Any randomly chosen bat produced by factory $F_1$ is defective with probability $0.5$ and any randomly chosen bat produced by factory $F_2$ is defective with probability $0.1$. One of the factories is chosen at random, and two bats are randomly purchased from the chosen factory. Let the labels on these purchased bats be $B_1$ and $B_2$. If $B_1$ is found to be defective, then the conditional probability that $B_2$ is also defective is equal to __________ (round off to 2 decimal places)