The BMW manager considered using a test by Mobis, a reputable supplier that specializes in testing

engine cooling systems. Mobis could carry out a test to determine whether or not the cooling system

was problematic. The test by Mobis indicated that there was a $90\%$ chance that the cooling system

was safe. The manager assumed that the test was perfectly accurate. And, BMW paid $$8$M for the

test. The manager has no idea how accurate the indication will be$.$ Your goal is to explain if BMW$$s

$$8$M payment was reasonable. Please answer the following sub problems.

Given that information, please explain if BMW$$s $$8$M payment was reasonable. To show your

answer, you must use a decision tree and clearly show how you calculate pro