If it is a fair game, the expected earnings should be $0.
Expected value per spin: $0.83 Is the game fair? No.
Practice makes perfect
The expected value from one spin depends on the probability of spinning each sector and their respective values. The probability of spinning a given sector is the ratio it occupies of the total spinner. We can find these ratios by dividing the sector angles by 360^(∘).
By calculating the product of each sector's probability and respective earnings, we get the expected value from that sector. If we add all of the sector's products, we get the expected earnings from one spin.
Event
P
Earnings
P * Earnings
Expected Earnings ($)
P($3)
1/3
3
1/3( 3)
1
P($5)
1/3
5
1/3( 5)
5/3
P(- $6)
1/4
- 6
1/4( - 6)
- 6/4
By adding all of the expected earnings per sector, we can get the expected earnings per spin.
