Question

what is expected value of the spinner? spinner image with sections labeled 2, 3, 6 multiple choice options: 3.7, 6, 11, 3.3 clear all

Explanation:

Step1: Determine probabilities

The spinner is divided into 3 equal parts, so each section has a probability of $\frac{1}{3}$.

Step2: Apply expected value formula

The expected value $E(X)$ is calculated as $E(X) = x_1P(x_1) + x_2P(x_2) + x_3P(x_3)$. Here, $x_1 = 2$, $x_2 = 3$, $x_3 = 6$, and $P(x_i)=\frac{1}{3}$ for all $i$.
So, $E(X)=2\times\frac{1}{3}+3\times\frac{1}{3}+6\times\frac{1}{3}$.

Step3: Calculate the sum

First, calculate each term: $2\times\frac{1}{3}=\frac{2}{3}$, $3\times\frac{1}{3} = 1$, $6\times\frac{1}{3}=2$. Then sum them: $\frac{2}{3}+1 + 2=\frac{2 + 3+6}{3}=\frac{11}{3}\approx3.7$.

Answer:

3.7