Question

Laila is visiting the grounds of an ancient burial site in the shape of a pyramid and is hoping to find old buried artifacts and sell them to a museum. Historians have told her that there is only 1 undiscovered artifact per side of the pyramid. She plans to look on all 4 sides of the pyramid and assumes that on each side there is a 50% chance of her finding that side's artifact independent of the other sides. The table below shows the resale value depending on how many artifacts she finds. What is the expected value of the resale value of the artifacts Laila finds?

Answer 1

The expected value of the resale value of the artifacts Laila finds is $87.5.

To calculate the expected value of the resale value of the artifacts Laila finds, we need to multiply the resale value of each possible outcome by its probability, and then sum up all these values.

Given that there is a 50% chance of finding an artifact on each side of the pyramid, the probability of finding an artifact on one side is 0.5. Since there are four sides, the probability of finding exactly one artifact is:

`(0.5)^1 * (1-0.5)^3` * 4C1

=
`4*(0.5)^1 * (0.5)^3`

=
`4*0.5^4`

= 0.25.

Similarly, the probability of finding exactly two artifacts is:

`(0.5)^2 * (1-0.5)^2` * 4C2

=
`6*(0.5)^2 * (0.5)^2`

=
`6*0.5^4`

= 0.375.

The expected value can be calculated as follows:

(0.25 * $50) + (0.375 * $100) + (0.375 * $200) + (0.0 * $500) = $87.5.