Question

Three labeled boxes containing red and white cricket balls are all mislabeled. It is known that one of the boxes contains only white balls and one only red balls. The third contains a mixture of red and white balls. You are required to correctly label the boxes with the labels red, white and red and white by picking a sample of one ball from only one box. What is the label on the box you should sample?

• A. White
• B. Red and White
• C. Red
• D. Not possible to determine from a sample of one ball

Hint:

Every label is wrong. Think about which box, when sampled, gives you a ball whose colour fixes the contents of that box immediately.

Answer 1

The Correct Option is B

Step 1: Use the fact that every label is wrong:
The box labelled "Red and White" cannot contain the mixture, so it holds only red balls or only white balls.

Step 2: Sample that box:
Draw one ball from the box labelled "Red and White". Its colour tells us the contents of this box exactly. Suppose the ball is red: this box is the "all red" box.

Step 3: Label the other two boxes:
The box labelled "White" is wrong, so it is not white; red is already taken, so it must be the mixed box. The box labelled "Red" is then the all-white box. If the sampled ball is white, the same reasoning works with red and white swapped.

Step 4: Why the other boxes fail:
If we sample the box labelled "White", it may contain red or mixed balls. A red ball could come from the all-red box or from the mixture, so we cannot decide. The same problem occurs with the box labelled "Red".

Final Answer:
The correct option is (2): Red and White