Question

at a carnival, you spin a spinner that has four equal - sized sections, each a different color: green, yellow, red, and blue. if you land on green, you win 2 points. if you land on yellow, red, or blue, you lose 1 point. write the expected value equation.
$e(v)=\frac{1}{a}(2)+\frac{1}{b}(c)+\frac{1}{d}(e)+\frac{1}{f}(g)$
$a = square$ x $rightarrow4$ $b=square$ x $rightarrow4$
$c=square$ x $rightarrow - 1$ $d=square$ x $rightarrow4$
$e=square$ x $rightarrow - 1$ $f=square$ x $rightarrow4$
$g=square$ x $rightarrow - 1$
the expected value of the number of points won on a spin is $square$ done

Explanation:

Step1: Identify probabilities and values

The spinner has 4 equal - sized sections, so the probability of landing on each section is $\frac{1}{4}$. Landing on green gives 2 points and landing on yellow, red, or blue gives - 1 point.

Step2: Write the expected - value formula

The expected - value formula for a discrete random variable is $E(X)=\sum_{i}p_ix_i$, where $p_i$ is the probability of the $i$th outcome and $x_i$ is the value of the $i$th outcome. Here, $E(V)=\frac{1}{4}(2)+\frac{1}{4}(-1)+\frac{1}{4}(-1)+\frac{1}{4}(-1)$.

Answer:

$a = 4$, $b = 4$, $c=-1$, $d = 4$, $e=-1$, $f = 4$, $g=-1$