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2 months ago

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

s. The container has 5 red tiles, 11 green tiles, and 4 blue tiles. If he draws a red tile, he moves forward 12 spaces. If he draws a green tile, he stays put. If he draws a blue tile, he moves backward 15 spaces. Use mathematical calculations to show whether or not the game is fair. That is, show whether Bob will hover around the same space (fair) or, over time, move away from the starting point (not fair). Show all of your calculations for full credit.

2 answers:

zzz [12.3K]2 months ago

7 0

The game is equitable.

Please refer to my attachment.

babunello [11.8K]2 months ago

5 0

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,

$E(Red\ tile)=\dfrac{5}{20}\times (+12)$

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

$E( Red\ tile)=\dfrac{60}{20}$

Likewise

$E(Green\ tile)=\dfrac{11}{20}\times (0)$

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

$E( Green\ tile)=0$

and

$E(Blue\ tile)=\dfrac{4}{20}\times (-15)$

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

$E(Blue\ tile)=\dfrac{-60}{20}$

Therefore, the overall expectation is:

$=E(Red\ tile)+E(Green\ tile)+E(Blue\ tile)\\\\\\=\dfrac{60}{20}+0-\dfrac{60}{20}\\\\=0$

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

Consequently, the game is fair.

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