Question

a company has an opportunity to bid on three contracts. determine which would be the best investment given the information in the table below.

probability of profit and loss by contract

contract	profit, probability of profit	probability to break even	loss, probability of loss
southwest	$60000, 35%	40%	$10000, 25%
california	$112000, 20%	40%	$40000, 40%

southeast
southwest
california
all contracts include a probability for loss.

Explanation:

Step1: Calculate expected profit for Southeast

The formula for expected value $E(X)$ is $E(X)=\sum_{i}x_ip_i$. For Southeast, $E_1 = 45000\times0.5+0\times0.3+( - 36000)\times0.2$.
$E_1=45000\times0.5 - 36000\times0.2=22500 - 7200 = 15300$.

Step2: Calculate expected profit for Southwest

For Southwest, $E_2=60000\times0.35 + 0\times0.4+( - 10000)\times0.25$.
$E_2=60000\times0.35-10000\times0.25 = 21000 - 2500=18500$.

Step3: Calculate expected profit for California

For California, $E_3 = 112000\times0.2+0\times0.4+( - 40000)\times0.4$.
$E_3=112000\times0.2-40000\times0.4=22400 - 16000 = 6400$.

Step4: Compare expected values

Since $18500>15300>6400$, Southwest has the highest expected profit.

Answer:

Southwest