Question

1. a spinner has equal regions labeled 0, 5, 10. what is the expected value?

Explanation:

Step1: Recall Expected Value Formula

The expected value \( E(X) \) for a discrete random variable is calculated as \( E(X)=\sum_{i} x_i P(x_i) \), where \( x_i \) are the possible values and \( P(x_i) \) are their corresponding probabilities.

Step2: Determine Probabilities

The spinner has 3 equal regions, so the probability of landing on each value (0, 5, 10) is \( P(0) = P(5) = P(10)=\frac{1}{3} \).

Step3: Calculate Expected Value

Substitute into the formula:
\( E(X)=0\times\frac{1}{3}+5\times\frac{1}{3}+10\times\frac{1}{3} \)
\( E(X)=\frac{0 + 5 + 10}{3}=\frac{15}{3}=5 \).

Answer:

5 (corresponding to the option "5")