a Given the angle measures, what is the probability of getting each field?
B
b Could you get any other value than 12?
A
a ≈ 4.42
B
b 12
Practice makes perfect
a Let's first determine the probabilities of getting each sector when you spin the wheel. We have to determine how large an area each sector occupies of the circle. We see that one sector has a 30^(∘) angle, so the remaining sector must have a 330^(∘) angle. With this information we can calculate the ratio that each sector occupies of the full circle.
If we multiply the ratio of each sector by their respective value and add the products, we get the expected value per spin.
Event
P
Value
P* Value
Expected Value
Heads
11/12
4
11/12* 4
44/12
Tails
1/12
9
1/12* 9
9/12
Let's add the expected values we will earn from the different sectors.
b Since there is only one sector with a value of 12, we will get this value every time we spin the spinner. Therefore, the expected, or rather guaranteed value is 12.
