# Sample Spaces of a Game

The game is played as follows. There are three doors. Behind each of two doors is a hamster. Behind the remaining door is a loaded BMW with a high performance engine. The host lets you choose a door. Before the host opens your chosen door, he always chooses one of the doors with a hamster, and asks you whether or not you want to change doors.

a) Complete the diagram in Tree Diagram. Replace “?” with outcome BMW or hamster, Save, and attach to your post.

b) For the case that the contestant keeps the original choice of door,

• Write the sample space of the 3 possible outcomes.
• How many of these outcomes are favorable?
• What is the probability of BMW = number of favorable outcomes/3.

c) For the case that the contestant changes doors,

• Write the sample space of the 3 possible outcomes.
• How many these outcomes are favorable?
• What is the probability of BMW = number of favorable outcomes/3.

d) What is the winning strategy, keep or change doors?

TREE DIAGRAM IS ATTACHED!!