for the wheel pictured on the right, assume that a person spins the pointer and is awarded the amount…

for the wheel pictured on the right, assume that a person spins the pointer and is awarded the amount indicated by the pointer. determine the persons expectation assuming the spinner has not yet been spun. what is the expectation? $ (simplify your answer. type an integer or a decimal.)

for the wheel pictured on the right, assume that a person spins the pointer and is awarded the amount indicated by the pointer. determine the persons expectation assuming the spinner has not yet been spun. what is the expectation? $ (simplify your answer. type an integer or a decimal.)

Answer

Explanation:

Step1: Determine probabilities

Since the wheel is divided into 3 equal - sized sections, the probability of landing on each section is $p=\frac{1}{3}$.

Step2: Identify outcomes

The outcomes are $x_1 = 12$, $x_2=-9$, $x_3 = - 20$.

Step3: Calculate expected value

The formula for the expected value $E(X)$ of a discrete - random variable is $E(X)=\sum_{i = 1}^{n}x_ip_i$. Here, $E(X)=12\times\frac{1}{3}+(-9)\times\frac{1}{3}+(-20)\times\frac{1}{3}$. First, calculate each product: $12\times\frac{1}{3}=4$, $(-9)\times\frac{1}{3}=-3$, $(-20)\times\frac{1}{3}=-\frac{20}{3}$. Then, sum them up: $E(X)=4 - 3-\frac{20}{3}=1-\frac{20}{3}=\frac{3 - 20}{3}=-\frac{17}{3}\approx - 5.67$.

Answer:

$-5.67$