KöMaL 2015 C1297

The main attractions of the show in a circus are the performances of a lion and an elephant. However, these performances cannot be accomplished if the animals are not in the mood. The lion appears on stage in $\frac{4}{5}$ of the shows, and the elephant only appears in $\frac{3}{4}$ of the shows. The circus is so lucky as to be able to show at least one of the animals in $99\%$ of the shows. What is the probability of both animals appearing in a show?