Question

an architect is considering bidding for the design of a new museum. the cost of drawing plans and submitting a model is $15,000. the probability of being awarded the bid is 0.1. if the architect is awarded the bid, she will make $150,000 minus the $15,000 cost for plans and a model. complete parts a. through b. below. a. what is the expected value in this situation? $0 (round to the nearest dollar) b. choose the statement below that best describes what this value means. a. in the long run, the architect would expect to break even. b. in the long run, the architect would expect to earn this amount. c. in the long run, the architect would expect to lose this amount. d. none of the above.

Explanation:

Step1: Calculate the expected value formula

The expected value \(E(X)\) formula is \(E(X)=\sum_{i}x_{i}p_{i}\). Here, there are two cases: winning the bid (\(x_1 = 150000 - 15000=135000\), \(p_1 = 0.1\)) and not winning the bid (\(x_2=- 15000\), \(p_2=1 - 0.1 = 0.9\)).

Step2: Substitute values into the formula

$$
LATEXBLOCK0
$$

The expected value of \(0\) means that on average, over many similar bidding situations (in the long - run), the architect neither makes a profit nor incurs a net loss. Breaking even implies that the average gain and loss cancel each other out.

Answer:

a. \(\$0\)
b. A. In the long run, the architect would expect to break even.