Given the angle measures, what is the probability of getting each region?
4.75
Practice makes perfect
Let's first determine the probabilities of hitting each region when doing a single spin. These probabilities depend on how large an area each region occupies. From the diagram, we see that two regions, - 3 and 10, both occupy a 90^(∘) angle. This means the remaining region occupies a 180^(∘) angle. Now we can calculate how much of the circle each region occupies.
If we multiply the probability of hitting each region by their respective value, and add the products, we get the expected value from one spin. Probability is calculated by dividing the number of favorable outcomes by the number of possible outcomes.
P=Number of favorable outcomes/Number of possible outcomes
With this information, we can calculate the expected value from each region when spinning the wheel once.
event
P
value
P * value
expected value
P(-3)
1/4
- 3
1/4( - 3)
- 3/4
P(10)
1/4
10
1/4( 10)
10/4
P(6)
1/2
6
1/2( 6)
6/2
By adding the expected values from each region, we get the expected value per spin.
