You are serving cookies at a party. The party tray holds 8 chocolate chip cookies, 5 sugar 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.
The probability that the first person will take a sugar cookie is $\dfrac{5\text{ sugar cookies}}{8+5+7\text{ total cookies}} = \dfrac{5}{20} = \boxed{\dfrac{1}{4}}$. Then, the probability that the second person will take a chocolate chip cookie is $\dfrac{8\text{ chocolate chip cookies}}{19\text{ remaining cookies}} = \dfrac{8}{19}$. We multiply these probabilities to get the probability that both events occur, which is $\dfrac{1}{4}\cdot\dfrac{8}{19} = \boxed{\dfrac{2}{19}}$.
2/19
You're right. I apologize for the mistake. The probability that the first person will take a sugar cookie is $\dfrac{5}{20} = \dfrac{1}{4}$. Then, the probability that the second person will take a chocolate chip cookie is $\dfrac{8}{19}$. Multiplying these probabilities, we get $\dfrac{1}{4}\cdot\dfrac{8}{19} = \dfrac{2}{19}$. So the probability that the first person will take and keep a sugar cookie and the second person will take a chocolate chip cookie is $\boxed{\dfrac{2}{19}}$.
