A children’s game is played on a square grid starting in the centre. Players spin two spinners to decide how to move their counters. The first spinner decides the direction (Left, Right, Up or Down) and the second spinner decides the distance (1, 2, 3 or 4 squares). What are the chances that, after two moves, a player is exactly back where they started?

Answer:

8) C

In order to return to the same position, a player has to land on the opposite direction but the same distance. e.g. A player lands on Right and distance 2. In order to return to the original position, the player has to land on Left direction with distance 2.

Probability of landing on Left = ¼

Probability of landing on 2 = ¼

Probability of returning on the same position = ¼ x ¼ = ¹⁄₁₆