An architect is considering bidding for the design of a new museum. The cost of drawing plans and submiting a model is \( \$ 14,000 \). The probability of being awarded the bid is 0.2 . If the architect is awarded the bid, she will make \( \$ 70,000 \) minus the \( \$ 14,000 \) cost for plans and a model. Complete parts a. through b. below. a. What is the expected value in this situation? \( \$ \square \) (Round to the nearest dollar.)

To find the expected value (EV) of the architect's bidding situation, we use the formula: \[ EV = (Probability \: of \: Winning \times Profit \: if \: Won) + (Probability \: of \: Losing \times Loss \: if \: Lost) \] If the architect wins, her profit is \( 70,000 - 14,000 = 56,000 \). If she loses, she incurs a cost of \( 14,000 \). Given the probabilities, we have: - Probability of winning: \( 0.2 \) - Probability of losing: \( 0.8 \) - Profit if she wins: \( \$ 56,000 \) - Loss if she loses: \( - \$ 14,000 \) Now, we can plug these values into the formula: \[ EV = (0.2 \times 56,000) + (0.8 \times -14,000) \] \[ EV = (11,200) + (-11,200) \] \[ EV = \$ 0 \] So, the expected value in this situation is \( \$ 0 \).