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 60% of the time. Seventy percent (75%) of her first serves and 85% of her second serves are good. What is the probability that Kim wins the point when she serves?

Question

anonymous · Answer

if it is confusing ( and it looks confusing to me) try it with numbers

lets say she serves $1000$ times, and $75\%$ are good.
then she has $.75\times 1000=750$ good serves, and of those $70\%$ she wins, so she wins $.7\times 750=525$ if the first serve is good
now we consider what happens if the first serve is not good

anonymous · Answer

i am not a tennis player, but i assume that she only gets a second serve if her first serve is bad, which would be $25\%$ of the time, and $.25\times 1000=250$ 
of those $250$ $85\%$ are good, so $.85\times 250=212.5$ second serves are good
of those, $60\%$ of the time she wins, making $.6\times 212.5=127.5$ wins

anonymous · Answer

her total wins is therefore $525+127.5=652.5$ take that out of $1000$ to get a probability of 
$$.6525$$

anonymous · Answer

if you want to repeat this without the $1000$ then compute 
$$.75\times .7+.25\times .85\times .6$$