Question

There is a spinner game in a fair. The player has to spin the spinner. If the spinner lands on the white sections, the player will win $10. Otherwise, the player will lose the entry fee which is $2. Check the fairness of the game.A)the game is fair B) the game is not fair, but favorable to the player.C) the game is not fair and not favorable to the player D) can’t be determined

Answer 1

We have a question about probability. Our approach is to obtain the mean amount that can be obtained for the possible outcomes.

Probability is derived as:

$\text{Probability = }\frac{\#\text{ of desired outcome}}{\#\text{ of total outcomes}}$

The probability, P of obtaining a white can be derived knowing:

# of desired outcome = 2

# of total outcome = 16

$P=\frac{2}{16}=\frac{1}{8}$

The average amount obtainable for spinning a white is:

$\mu=\frac{1}{8}\times\text{ \ 10=\ 1.25}$

The probability, Q of obtaining any other color can be derived knowing:

# of desired outcome = 14

# of total outcome = 16

$P=\frac{14}{16}=\frac{7}{8}$

The average amount obtainable for spinning any other color is:

$\mu=\frac{7}{8}\times\text{ \ 2=\ 1.75}$

Net gain on average: Average amount gained - Average amount lost

$\text{ Net gain = \ 1.25 - \ 1.75 = -\ 0.50}$

On average, the player loses 50 cents. That makes it unfavorable for him.

OPTION C