Consider the following scenario. Bob is playing a board game where he blindly picks a tile from a container and moves some space

Answer:

Indeed, the game is balanced.

Step-by-step explanation:

To verify the fairness of the game, we need to demonstrate that the total expectation amounts to zero.

This means Bob will mostly remain in the same vicinity.

There are 20 tiles in total within the container.

(As 5 red tiles + 11 green tiles + 4 blue tiles = 20 tiles)

The likelihood of selecting a red tile is:

     Number of red tiles/Total number of tiles

     =  5/20

Furthermore, the likelihood of selecting a green tile is:

   Number of green tiles/Total number of tiles

 = 11/20

Additionally, the likelihood of selecting a blue tile is:

   Number of blue tiles/Total number of tiles

     =  4/20

Let E represent the expectation of an event.

Thus,

Because when a red tile is picked, Bob moves forward 12 spaces.

Likewise

Since when a green tile is selected, Bob does not move.

and

When a blue tile is chosen, Bob moves back 15 spaces.

Therefore, the overall expectation is:

       This indicates that he will remain in approximately the same position.

             Consequently, the game is fair.