Question

You want to go to a concert in Detroit, but you have only $80. The cost of driving will be $30. When you get to the concert, there's a 40% chance you'll be able to get a ticket for $50, and a 60% chance that tickets will cost more than $50. If it's worth $130 to you to go to the concert, should you drive to Detroit to attend this concert? To solve, use a decision tree.

Answer 1

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.