Final answer:
Using a decision tree, we can calculate the expected cost of attending the concert in Detroit and determine whether it's worth driving there.
Step-by-step explanation:
To determine whether it is worth driving to Detroit to attend the concert, we need to calculate the expected value of attending the concert. We can use a decision tree to represent the different possibilities.
If you drive to Detroit, there is a 40% chance that tickets will cost $50, and a 60% chance that tickets will cost more than $50. We multiply the probability by the cost of the tickets to calculate the expected cost of the tickets.
If tickets cost $50, the expected cost is 0.4 * $50 = $20. If tickets cost more than $50, the expected cost is 0.6 * $130 = $78.
The total expected cost is the sum of the expected cost of driving ($30) and the expected cost of the tickets ($20 + $78 = $98). Since the total expected cost is less than your budget of $80, it is worth driving to Detroit to attend the concert.