Difference between revisions of "2020 AMC 12B Problems/Problem 16"
(Created page with "==Problem== An urn contains one red ball and one blue ball. A box of extra red and blue balls lie nearby. George performs the following operation four times: he draws a ball f...") |
(→Problem) |
||
| Line 2: | Line 2: | ||
An urn contains one red ball and one blue ball. A box of extra red and blue balls lie nearby. George performs the following operation four times: he draws a ball from the urn at random and then takes a ball of the same color from the box and returns those two matching balls to the urn. | An urn contains one red ball and one blue ball. A box of extra red and blue balls lie nearby. George performs the following operation four times: he draws a ball from the urn at random and then takes a ball of the same color from the box and returns those two matching balls to the urn. | ||
After the four iterations the urn contains six balls. What is the probability that the urn contains three balls of each color? | After the four iterations the urn contains six balls. What is the probability that the urn contains three balls of each color? | ||
| − | <math>\textbf{(A)}\ \frac{1}{6} \qquad\textbf{(B)}\ \frac{1}{ | + | <math>\textbf{(A)}\ \frac{1}{6} \qquad\textbf{(B)}\ \frac{1}{5} \qquad\textbf{(C)}\ \frac{1}{4} \qquad\textbf{(D)}\ \frac{1}{3} \qquad\textbf{(E)}\ \frac{1}{2}</math> |
Revision as of 21:28, 7 February 2020
Problem
An urn contains one red ball and one blue ball. A box of extra red and blue balls lie nearby. George performs the following operation four times: he draws a ball from the urn at random and then takes a ball of the same color from the box and returns those two matching balls to the urn.
After the four iterations the urn contains six balls. What is the probability that the urn contains three balls of each color?
