An architect is considering bidding for the design of a new museum. The cost of drawing plans and sulbmitting 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? \( \$ 0 \) (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 earn this amount. B. In the long run, the architect would expect to lose this amount. C. In the long run, the architect would expect to break even. D. None of the above.

To find the expected value, we consider the outcomes based on the probability of winning the bid. The profit if awarded the bid is \( \$ 70,000 - \$ 14,000 = \$ 56,000 \). The probability of being awarded the bid is 0.2, and the probability of not being awarded the bid is 0.8, which results in a loss of \( \$ 14,000 \). Now, we compute the expected value (EV): \[ EV = (0.2 \times 56,000) + (0.8 \times -14,000) \] \[ = 11,200 - 11,200 = 0 \] So, the expected value is \( \$ 0 \). For part b, the best statement that describes what this value means is: C. In the long run, the architect would expect to break even. Now let's make this engaging! Imagine you're standing at the crossroads of creativity and risk in architecture! If you were to imagine this scenario as a thrilling game of chance, you'd find that the architect's gamble is akin to rolling the dice. With a \(20\%\) chance of scoring a grand prize, it might seem like a sweet deal until you'd realize that taking the plunge also means facing some financial losses. In the end, it all balances out; you might not gain or lose, like a perfectly balanced seesaw! The art of designing may be timeless, but let's talk about strategy! If you’ve ever taken a deep dive into the world of bids, you probably know that preparing for project proposals is a tightrope walk between expenses and potential profits. The ultimate trick? Ensure you're budgeting for those costs, but also consider enhancing your proposal with innovative flair. Sometimes, a little more creativity can tip the odds in your favor, turning a simple project into a masterpiece worthy of a museum!