Question

akira is playing a game where she will spin a number on a spinner labeled 1-8. she can earn points for spinning certain numbers. the probability and point values for each number is below. what is the expected number of points to be earned for a spin?

number spun, probability and points

\

$$\begin{tabular}{|l|l|l|} \\hline \\text{number spun} & \\text{probability} & \\text{points} \\\\ \\hline 1 & 0.125 & 20 \\\\ \\hline 2, 4, 6, 8 & 0.5 & 2 \\\\ \\hline 3, 5 & 0.25 & 0 \\\\ \\hline 7 & 0.125 & 6 \\\\ \\hline \\end{tabular}$$

(a) 7
(b) 4.75
(c) 1.4375
(d) 4.25

Explanation:

Define the expected value formula

$$ E(X) = \sum x_i \cdot P(X = x_i) $$

Calculate the products of points and probabilities

$$
LATEXBLOCK0
$$

Sum the products to find the expected value

$$ E(X) = 2.5 + 1.0 + 0.0 + 0.75 = 4.25 $$

Answer:

• 7
• 4.75
• 1.4375
• 4.25 (Correct answer)