You are serving cookies at a party. The party tray holds 8 chocolate chip cookies, and 7 oatmeal raisin cookies. What is the probability that the first person will take and keep a sugar cookie and the second person will take a chocolate chip cookie? Write your answer as a simplified fraction.
There are a total of 8 + 7 = <<8+7=15>>15 cookies on the tray.
The probability that the first person takes a sugar cookie is 8/15.
After the first person takes a sugar cookie, there are 14 cookies remaining on the tray.
The probability that the second person takes a chocolate chip cookie is 8/14.
Therefore, the probability that the first person takes a sugar cookie and the second person takes a chocolate chip cookie is (8/15) * (8/14) = 64/210.
The simplified fraction of 64/210 is 32/105. Answer: \boxed{\frac{32}{105}}.