It is a hot morning in February in Sydney.$$ However, some dark clouds are appearing outside as well.$$ It might rain and you are thinking about taking an umbrella with you. Considering the history of weather in Sydney, there is a $30\%$ chance of rain on any given day in February.$$ Furthermore, on days when it does in fact rain, $95\%$ of the time there are dark clouds that roll in during the morning.$$ But, on days when it does not rain, $25\%$ of the time there are dark clouds that roll in during the morning. Given that there are dark clouds rolling in$,$ what is the chance that it will rain?