Expected Value Assignment

A real estate agent spends $1,500 on advertising for three months to sell an average house. If the house sells in three months, the agent earns $9,000. Otherwise, he loses the listing and earns nothing. If there is a 40% chance that the house will sell in three months, what is the expected revenue for the real estate agent? $2,000 $2,100 $3,200 $3,600

$2,100

Roll a number cube. If the number cube comes up odd, you win the same number of points as the number on the cube. If the number comes up even, you lose 4 points.What is the expected number of points per roll? -0.25 -0.5 0 0.25 0.5

-0.5

The expected value of the number of points for one roll is: 0 1 3 6

0

In each turn of a game you toss two coins. If 2 heads come up, you win 2 points and if 1 head comes up you win 1 point. If no heads come up, you lose 3 points.What is the expected value of the number of points for each turn? -0.25 0 0.25 0.5 This game is

0.25 favorable

In basketball, Shaquille makes 40% of his free throw attempts. He goes to the free throw line to shoot one-and-one (if he makes the first shot, he gets to shoot one more). He scores 1 point per free throw. What is the expected value of the number of points he will score? 0.064 0.24 0.56 0.80

0.56

What is the expected number of female children in a family with three children? 1 1.5 2 2.5

1.5

You play a game in which two coins are flipped. If both coins turn up tails, you win 1 point. How many points would you need to lose for each of the other outcomes so that the game is fair? 1/4 1/3 1 4/3

1/3

You are considering two investment opportunities. For investment A there is a 25% chance that you lose $20,000, a 50% chance that you break even, and a 25% chance that you make $80,000. For investment B there is a 30% chance that you lose $50,000, a 50% chance that you break even, and a 20% chance that you make $180,000. Based on the expected value of each, which investment should you make? The expected value of investment A is The expected value of investment B is $. Based on the expected value, you should make

15,000 21,000 Investment B

You toss two number cubes. If a sum of 7 or 11 comes up, you get 7 points, if not you lose 2 points.The probabilities for each of the sums is:P(2) = 1/36 P(3) = 1/18 P(4) = 1/12 P(5) = 1/9P(6) = 5/36 P(7) = 1/6 P(8) = 5/36 P(9) = 1/9P(10) = 1/12 P(11) = 1/18 P(12) = 1/36 The probability of a sum of 7 or 11 is: 1/36 1/18 2 / 9 1/36

2/9

A company is considering making a new product. They estimate the probability that the new product will be successful is 0.75. If it is successful it would generate $240,000 in revenue. If it is not successful, it would not generate any revenue. The cost to develop the product is $196,000. Use the profit (revenue − cost) and expected value to decide whether the company should make this new product.

P = $240,000 - $196,000 = $44,000. The expected value is a weighted average of each possible value weighted by its probability. EV = ($44,000)(0.75) + ($-196,000)(0.25) = $-16,000. The expect average profit is $-16,000. The company should not make the product.