Grades 11-12 Video Solutions 2011-11&12 Video Solutions 2011 problem24

11&12 Video Solutions 2011 problem24

Video Transcription

Video Summary

The problem involves determining the number of marbles, \( M \), in a bowl with red and green marbles such that the probability of picking two marbles of the same color is \( \frac{1}{2} \). By expressing \( M \) as \( R + G \) and using probability calculations, the algebraic manipulation shows that \( M \) must be a perfect square. After analyzing the equation \((2G + M)^2\), it is concluded that the total number of marbles, \( M \), has to be 81, which is the only perfect square among the provided choices.

Keywords

marbles

probability

perfect square

algebraic manipulation

probability calculation