Question

g.pr.10.5 (mc)

a coin is tossed 3 times. you earn 2 points if there is only one head, 5 points for two heads, and 10 points for 3 heads. the probability for these possibilities is below. what is the expected number of points you would earn?

number of heads, probability and points

\

$$\begin{tabular}{|c|c|c|c|c|} \\hline number of heads & 0 & 1 & 2 & 3 \\\\ \\hline probability & \\frac{1}{8} & \\frac{3}{8} & \\frac{3}{8} & \\frac{1}{8} \\\\ \\hline points & 0 & 2 & 5 & 10 \\\\ \\hline \\end{tabular}$$

• 0.375
• 4.625
• 3.875
• 0.333

Explanation:

Define the expected value formula

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

Substitute the given points and probabilities

$$ E(X) = 0 \cdot \frac{1}{8} + 2 \cdot \frac{3}{8} + 5 \cdot \frac{3}{8} + 10 \cdot \frac{1}{8} $$

Calculate the final expected value

$$
LATEXBLOCK0
$$

Answer:

• (A) 0.375
• (B) 4.625
• (C) 3.875 (Correct answer)
• (D) 0.333