On Monday, Wile E. is expecting to receive a package (package A) from Acme Distributing containing an anvil valued at $200. Based on his past experience with the delivery service, Wile E. estimates that this package has a 3% chance of being lost in shipment.

 

A) What is the random variable in this scenario?

 

B) Is Wile E.'s probability estimate an "a priori" (theoretical) probability or statistical (empirical) probability? Justify your answer. 

 

C) Create a table and derive the probability distribution for total dollar losses in this case. Note that this is total dollar losses, not the number of losses. Make sure you label your table correctly.

 

D) Is this an example of a compound/joint outcome or mutually exclusive event? Explain why.

 

E) On Friday, Wile E. expects another package (package B) from Acme Distributing containing dynamite valued at $300. This package has a 10% chance of being lost in shipment.

What are each of the possible outcomes for Wile E.'s total dollar amount of losses for packages A (anvil) and B (dynamite)? For each dollar amount of loss you identify, describe under what circumstances it would occur. In other words, what has to happen in order for each dollar amount of losses to occur? Please note that this asks about total dollar amount of losses for each outcome, not number of losses.

 

F)  For each of the possible outcomes you identify in your answer to the question above, derive the probability of the outcome occurring. Show calculations; display three decimal places.