Question

Isn't there only two ways to choose the other point because if the left secondtobottom node is red, the bottom is green or yellow. The green and yellow have the same number of ways, so assume that the bottom is yellow. Then the right secondtobottom node is either green or red, so the fraction is \(\frac{1}{2}.\)

@spaceblastxy1428 This is interesting. There are twice as many ways for the two secondtobottom nodes to be different colors rather than the same color, so the ratio of ways for them to be different to ways for them to be the same color is \( 2 : 1.\) The question asks for the fraction of the total ways that have the secondtobottom nodes the same color, so the answer is \( \boxed{ \frac{1}{3}}.\)