A construction company is planning to bid on a buliding contract. The bid costs the company
. The probability that the bid is accepted is . If the bid is accepted, the company will make
minus the cost of the bid.
a. What is the expected value in this situation?
(Round to the nearest dollar.)

Ask by Schneider Huang. in the United States

Mar 20,2025

Question

A construction company is planning to bid on a buliding contract. The bid costs the company
. The probability that the bid is accepted is . If the bid is accepted, the company will make
minus the cost of the bid.
a. What is the expected value in this situation?
(Round to the nearest dollar.)

Ask by Schneider Huang. in the United States

Mar 20,2025

UpStudy AI · Accepted Answer

To find the expected value of the situation, we can use the formula for expected value (EV):

$$
EV = (P(\text{accepted}) \times \text{profit if accepted}) + (P(\text{not accepted}) \times \text{loss if not accepted})
$$

### Step 1: Identify the known values
- Cost of the bid: $$ C = 1600 $$
- Probability of acceptance: $$ P(\text{accepted}) = \frac{1}{5} $$
- Probability of not acceptance: $$ P(\text{not accepted}) = 1 - P(\text{accepted}) = 1 - \frac{1}{5} = \frac{4}{5} $$
- Profit if accepted: $$ \text{profit if accepted} = 25500 - C = 25500 - 1600 = 23900 $$
- Loss if not accepted: $$ \text{loss if not accepted} = -C = -1600 $$

### Step 2: Calculate the expected value
Now we can substitute these values into the expected value formula:

$$
EV = \left(\frac{1}{5} \times 23900\right) + \left(\frac{4}{5} \times -1600\right)
$$

### Step 3: Perform the calculations
1. Calculate the first term:
   $$
   \frac{1}{5} \times 23900 = 4780
   $$

2. Calculate the second term:
   $$
   \frac{4}{5} \times -1600 = -1280
   $$

3. Combine the results:
   $$
   EV = 4780 - 1280 = 3500
   $$

### Final Answer
The expected value in this situation is $$ \$ 3500 $$.
The expected value is \$3500.

A construction company is planning to bid on a buliding contract. The bid costs the company
. The probability that the bid is accepted is . If the bid is accepted, the company will make
minus the cost of the bid.
a. What is the expected value in this situation?
(Round to the nearest dollar.)

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Probability Questions

A construction company is planning to bid on a buliding contract. The bid costs the company . The probability that the bid is accepted is . If the bid is accepted, the company will make minus the cost of the bid. a. What is the expected value in this situation? (Round to the nearest dollar.)

Upstudy AI Solution

Answer

Solution

Mind Expander

Related Questions

Latest Probability Questions

A construction company is planning to bid on a buliding contract. The bid costs the company
. The probability that the bid is accepted is . If the bid is accepted, the company will make
minus the cost of the bid.
a. What is the expected value in this situation?
(Round to the nearest dollar.)