a company has an opportunity to bid on three contracts. determine which would be the best investment given…

a company has an opportunity to bid on three contracts. determine which would be the best investment given the information in the table below.\n\nprobability of profit and loss by contract\n| contract | profit, probability of profit | probability to break even | loss, probability of loss |\n|--|--|--|--|\n| southeast | $45000, 50% | 30% | $6000, 20% |\n| southwest | $60000, 35% | 40% | $10000, 25% |\n| california | $112000, 20% | 40% | $40000, 40% |\n\nsoutheast\nsouthwest\ncalifornia\nall contracts include a probability for loss.

a company has an opportunity to bid on three contracts. determine which would be the best investment given the information in the table below.\n\nprobability of profit and loss by contract\n| contract | profit, probability of profit | probability to break even | loss, probability of loss |\n|--|--|--|--|\n| southeast | $45000, 50% | 30% | $6000, 20% |\n| southwest | $60000, 35% | 40% | $10000, 25% |\n| california | $112000, 20% | 40% | $40000, 40% |\n\nsoutheast\nsouthwest\ncalifornia\nall contracts include a probability for loss.

Answer

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