2. An investment counselor calls with a hot stock tip. He believes that if the e
ID: 3362251 • Letter: 2
Question
2. An investment counselor calls with a hot stock tip. He believes that if the economy remains strong, the investment will result in a profit of $40,000. If the economy grows at a moderate pace, the investment will result in a profit of $10,000. However, if the economy goes intorecession, the investment will result in a loss of $40,000. You contact an economist who believes there is a 20% probability the economy will remain strong, a 70%
probability the economy will grow at a moderate pace, and a 10% probability the economy will slip into recession. What is the expected profit from this investment?
The expected profit is $__?___ (Type an integer or a decimal.)
3. In the game of roulette, a player can place a $6 bet on the number 27 and have a 1/38 probability of winning. If the metal ball lands on 27, the player gets to keep the $6 paid to play the game and the player is awarded $210. Otherwise, the player is awarded nothing and the casino takes the player's $6. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose?
The expected value is $ __?___ (Round to the nearest cent as needed.)
The player would expect to lose about $ __?___ (Round to the nearest cent as needed.)
Explanation / Answer
Probability distribution of Profit
X ----------- P(X)
40000 -------- 20% = 0.20
10000 -------- 70% = 0.70
-40000 ------- 10% = 0.10
Total ----------------- = 1.00
Expected profit = E(X) = sigma xp
= (40000*0.20) + (10000*0.70) + (- 40000*0.10)
= 8000 + 7000 - 4000
= $11000
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