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The way the game is played out is as follows. There is a goat behind two doors a

ID: 3047701 • Letter: T

Question

The way the game is played out is as follows. There is a goat behind two doors and a BMW behind one door. The host lets you choose a door. Assume you choose door #1. Before he opens door #1 to let you see what you have chosen, he opens one of the remaining doors, say door #3, to reveal a goat (he will always open the remaining doors that has a goat), and asks you whether or not you want to change your choice.

a) Make a tree diagram of the possible sequences of events by completing the following diagram

b) For the case that the contestant does not change doors, list the sample space of possible outcomes.

c) For the case that the contestant changes doors, list the sample space of possible outcomes.

d) For each of the sample spaces in b) & c), how many outcomes are there and how many outcomes are favorable?

e) What do you tell the host?

Contestant swiches door Contestant picks correct door Monty opens a wrong door Contestant does not switch door Escalade Contestant suwitches door Contestest picks a wrong door Monty opens a wrong door Contestant doesnot switch door Contestant suwitches door Contestant picks other wrong door Monty opens a wrong door Contestant does not switch door Sample space from switching doors Sample Space from no switching doors

Explanation / Answer

Sample space from not switching doors-

The options from top to below are-

a) Wrong

Wrong

b) On the right, the answers from top to below are

Wrong

BMW

BMW

c) No switch - 3 outcomes. Probability of BMW=13

Switch- 3 outcomes Probability of BMW=2/3

d) Switch the door is the best option