$4.$ Serena Williams serves. In her loss in the $2019$ Wimbledon finals $($against Simona Halep$),$ Serena Williams made $32$ of her $47$ first serves and committed one double fault.

a$.$ Find the probability that her first serve is good.

b$.$ Find the conditional probability of double faulting, given that her first serve resulted in a fault.

c$.$ On what percentage of her service points does she double fault?