Question

for each spinner below, calculate the expected value

Explanation:

Step1: Calculate the probability of each number

The total degrees in a circle is \(360^{\circ}\).
For the number \(3\): The central angle is \(360 - 30=330^{\circ}\), so the probability \(P(3)=\frac{330}{360}=\frac{11}{12}\)
For the number \(9\): The central angle is \(30^{\circ}\), so the probability \(P(9)=\frac{30}{360}=\frac{1}{12}\)

Step2: Use the expected - value formula \(E(X)=\sum_{i}x_{i}P(x_{i})\)

Here \(x_1 = 3\), \(P(x_1)=\frac{11}{12}\) and \(x_2 = 9\), \(P(x_2)=\frac{1}{12}\)

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Answer:

\(3.5\)