Question

expected value: probability worksheet
expected value is a quantity used to determine expected results (gain or loss) over the long term. to calculate expected value, you identify each possible outcome for a scenario and multiply each outcomes probability by its respective the net earning or loss prediction.
$e(x)=p_1cdot a_1 + p_2cdot a_2+p_3cdot a_3+ldots+p_ncdot a_n$

$p_n$	the probability that outcome $n$ will occur
$a_n$	the net amount earned or lost if outcome $n$ occurs
$n$	the event number $(1,2,3,ldots n)$

for each of the following problems, calculate the expected value.

1. starbucks is considering opening a new store near campus. the company has estimated that there is a 60% chance that they will earn a $45,000 profit, a 15% chance that they will break even, and a 25% that they will lose $27,500 in the first year. using the table below, determine starbucks expected value.

$n$	possible outcomes	$p_n$	$a_n$	$p_ncdot a_n$
1	profit
2	break even
3	loss

|expected value|

Explanation:

Step1: Identify probabilities and amounts

$P_1 = 0.6$, $A_1=45000$, $P_2 = 0.15$, $A_2 = 0$, $P_3=0.25$, $A_3=- 27500$

Step2: Calculate $P_n\cdot A_n$ products

$P_1\cdot A_1=0.6\times45000 = 27000$, $P_2\cdot A_2=0.15\times0 = 0$, $P_3\cdot A_3=0.25\times(-27500)=-6875$

Step3: Sum products for expected value

$E(x)=27000 + 0-6875=20125$

Answer:

$20125$