IKMC 2027 - Grades 9-10 - Self-study SET 2 - Thematic Batch 3 Question 14

Question 14

A rectangular cuboid has dimensions 2 × 2 × 1. Two ants start at opposite ends of a space diagonal, as shown. Each travels one unit along one of the drawn lines. What is the probability that their final positions lie on a common face of the cuboid?

Question illustration

$\frac{2}{9}$
$\frac{1}{3}$
$\frac{4}{9}$
$\frac{5}{9}$
$\frac{2}{3}$