An architect is considering bidding for the design of a new museum. The cost of drawing plans
and submiting a model is . The probability of being awarded the bid is 0.2 . If the
architect is awarded the bid, she will make minus the cost for plans and a
model. Complete parts a. through b. below.
a. What is the expected value in this situation?
(Round to the nearest dollar.)

Ask by Wilson Schofield. in the United States

Mar 20,2025

Question

An architect is considering bidding for the design of a new museum. The cost of drawing plans
and submiting a model is . The probability of being awarded the bid is 0.2 . If the
architect is awarded the bid, she will make minus the cost for plans and a
model. Complete parts a. through b. below.
a. What is the expected value in this situation?
(Round to the nearest dollar.)

Ask by Wilson Schofield. in the United States

Mar 20,2025

UpStudy AI · Accepted Answer

Let the outcomes be defined as follows:

- If the architect is awarded the bid (with probability $$0.2$$), the net profit is 
  $$
  \$70{,}000 - \$14{,}000 = \$56{,}000.
  $$
- If she is not awarded the bid (with probability $$0.8$$), she loses the cost, i.e., 
  $$
  -\$14{,}000.
  $$

The expected value $$E$$ is calculated as:
$$
E = (0.2)(\$56{,}000) + (0.8)(-\$14{,}000).
$$

Calculating each term:
$$
(0.2)(\$56{,}000) = \$11{,}200,
$$
$$
(0.8)(-\$14{,}000) = -\$11{,}200.
$$

Adding these values:
$$
E = \$11{,}200 + (-\$11{,}200) = \$0.
$$

Thus, the expected value is 
$$
\$0.
$$
The expected value is \$0.

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