Question

Kim has a strong first serve; whenever it is good (that is, in) she wins the point 70% of the time. Whenever her second serve is good, she wins the point 57% of the time. Seventy percent of her first serves and 76% of her second serves are good. What is the probability that Kim wins the point when she serves? ...?

Answer 1

Lets put ti this way:
P[1st serve good & wins point] = 60% * 70% = 42% = A 
P[2nd serve good & wins point] = 40% * 76% *57% = 17.328% = B 

1. P[win point] = A+B = C = 59.328% <------- 
2. P[1st serve good | win point ] = A/C = 42 / 59.328 = 0.707 or 70.7%
Please remember that 2nd serve come into use only if 1st serve is not good