Jane has two tennis serves, a hard serve and a soft serve. Her hard serve is in (a good serve) 50% of the time, and her soft serve is in (good) 75% of the time. If her hard serve is in she wins 75% of her points. If her soft serve is in she wins 50% of her points. Since she is allowed to reserve one time if her first serve is out, what should her serve strategy be? That is, should she serve hard followed by soft; both hard; soft followed by hard; or both soft?
Please show formula used to solve this problem.

For any combination of soft and hard serves;

P(winning the point) = P(1st serve in) x P (1st serve winning) + P(1st serve out) x P(2nd serve in) x P(2nd serve winning)

I'll let you fill in the values to find the best strategy