Question

A farmer wants to decide if he should plant beets or sweet potatoes. No matter what he plants he will get either a good, average, or bad crop yield. For beets, a good yield will give him a profit of $5,000, average will profit $3,000 and, and a bad yield will give a profit of $1,000. For sweet potatoes, the profit for good, average, and bad yields are as follows: $6,000, $3,000, and $0. For either crop, the probability of good yield is 0.4, the probability of average yield is 0.5 and the probability of a bad yield is 0.1.What are the outcomes sweet potatoes?

a. $3,000, $1,000,0$
b. $6,000, $3,000, $0
c. $6,000*.4, $3,000*.5, $0*.1
d. $5,000*.4, $3,000*0.5, $1,000*.1

Answer 1

The correct outcomes for sweet potatoes, based on a good, average, and bad yield, are $6,000, $3,000, and $0 respectively. These figures are before considering the probabilities of each yield occurring.

Step-by-step explanation:

The student has presented a scenario where a farmer is deciding between planting beets or sweet potatoes and wants to know the outcomes for sweet potatoes given the probabilities of good, average, and bad yields. Since the probabilities for either crop are given as 0.4 for a good yield, 0.5 for an average yield, and 0.1 for a bad yield, and the corresponding profits for sweet potatoes are $6,000, $3,000, and $0 respectively, we can look at the potential outcomes for each scenario.

• 
  
• Good yield profit: $6,000 with a probability of 0.4
• 
  
• Average yield profit: $3,000 with a probability of 0.5
• 
  
• Bad yield profit: $0 with a probability of 0.1

The expected profit for planting sweet potatoes is a weighted average of the three scenarios, which can be expressed as $6,000*0.4 + $3,000*0.5 + $0*0.1.

The correct answer from the options provided is b. $6,000, $3,000, $0, which represents the profits associated with good, average, and bad yields for sweet potatoes without considering the probabilities.

The final answer in a two line explanation to provide a 300-word response would be: The outcomes for planting sweet potatoes are based on the profits for each type of yield, which are $6,000 for a good yield, $3,000 for an average yield, and $0 for a bad yield. These outcomes correspond to the given probabilities of 0.4, 0.5, and 0.1 respectively.