Question 152112This question is from textbook
: I would greatly appreciate your help with this word problem.
Jonah was visiting his grandfather, who has a large jellybean collection. When he asked if he could have some he said yes, if he could solve a problem for him. He told him that he has three jars, containing either all red jellybeans, all green jellybeans or red and green jellybeans. Each jar is covered so that no one can see the color of the jellybeans. One jar is labeled red, the second green and the third red-green. The catch was that none of the jars was correctly labeled. He could reach into one jar, remove one jellybean and look at it. He would then have to tell him the correct color of the jellybeans in each jar. Which jar should he choose a jellybean from and how does that help him in labeling the jars correctly.
Initally, I thought that if he pulled from the jar labeled red but got a green jellybean then he would know how to label the jars. This doesn't ring true since there is a mixed red-green jar.
Jar Red = either green or mixed beans
Jar Green = either red or mixed beans
Jar Red-Green = either red or green beans
Thank you
This question is from textbook
Answer by mducky2(62)   (Show Source):
You can put this solution on YOUR website! The fact that none of the jars were correctly labeled is actually the key to solving this problem.
You know that, whichever jar you choose, you have to know exactly which color belongs in that jar. If you choose the red-label or green-label jars, no matter what color jelly bean you pick, you aren't sure whether it came from the mixed jar or one of the pure color jars.
However, if you pick from the mixed-label jar, since you know that the jar is incorrectly labeled, whichever color you choose must be real color of the jar. If you pick a red jelly bean, the mixed-label jar is actually the red jar. If you pick a green jelly bean, the mixed-label jar is actually the green jar.
Let's say that you picked a red jelly bean from this mixed-label jar. If you look around for the green-label jar, since the label has to be wrong, you already knew that it has to either be mixed or the red jar. Since it can't be the red jar (you just picked from the real red jar), it has to be the mixed jar. Therefore, the last jar, the red-label jar, has to be the green jar. Now you know the true colors of all the jars.
The same logic works if you picked a green jelly bean from the mixed-label jar. From that, the red-label jar would have to be the mixed jar, and the green-label jar would have to be the red jar.
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