QuestionFor the wheel pictured on the right, assume that a person spins the pointer and is awarded the amount indicated by the pointer. Determine the person's expectation assuming the spinner has not yet been spun.
What is the expectation? \$$\square$ (Simplify your answer. Type an integer or a decimal.)

Studdy Solution
Use the formula for expectation:
$$E(X) = \sum ( \text{value} \times \text{probability} )$$
Calculate the expected value:
$$E(X) = 10 \times \frac{1}{3} + (-6) \times \frac{1}{3} + (-21) \times \frac{1}{3}$$
$$E(X) = \frac{10}{3} - \frac{6}{3} - \frac{21}{3}$$
$$E(X) = \frac{10 - 6 - 21}{3}$$
$$E(X) = \frac{-17}{3}$$
$$E(X) = -5.67$$
The expectation is:
$$\boxed{-5.67}$$