Answer: The expected value is 12.44
Step-by-step explanation:
The expected value can be calculated as:
EV = ∑xₙ*pₙ
Where xₙ is the n-th outcome. For the case of the spinner we have 3 possible outcomes:
x₁ = 8
x₂ = 6
x₃ = 24
And pₙ is the probability of the n-th event.
For the case of the spinner, the probability of each section will be equal to the quotient between the degrees of each arc, and the total number of degrees in a circle (360°).
First, we can see that for outcome = 8, the angle is a right angle, then it is equal to 90°, then the probability of this event will be:
p₁ = 90°/360° = 0.25
For outcome = 24, we have an angle of 120°, then the probability for this event is:
p₃ = (120°/360°) = 0.33
And the angle for the third arc must be such that:
90° + 120° + A = 360°
then:
A = 360° - 90° - 120° = 150°
Then the probability for the outcome = 6 is:
p₂ = (150°/360°) = 0.42
Now we can find the expected value as:
EV = (8*0.25 + 6*0.42 + 24*0.33) = 12.44
