1. A Problem that will delight your fancy
An Engineering Management Bonus
A Problem that will delight your fancy
How delightful.
The Game Show Problem
A game show involves members of the public or celebrities playing a game for points or prizes.

2. The Game Show Problem
Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?
p = 1/3 p = 1/ p = 1/3

3. Switch Doors!
Opening a losing door does not affect the probability of 1/3 that the car is behind the player's initially chosen door.
As there remains only one other door, the probability that this door conceals the car must be 2/3 (1 - 1/3).
Switching increases the chances of winning the car from 1/3 to 2/3. 3 1 2
p = 1/ p = 2/3 open door

4. The Six Possibilities First 3 games - you select door #1 and switch
Second 3 games – you select door 1 and do not switch
Door1 Door2 Door3
Auto Goat Goat
switch and lose.
Door1 Door2 Door3
Auto Goat Goat
stay and win.
Door1 Door2 Door3
Goat Auto Goat
switch and win.
Door1 Door2 Door3
Goat Auto Goat
stay and lose.
Door1 Door2 Door3
Goat Goat Auto
switch and win.
Door1 Door2 Door3
Goat Goat Auto
stay and lose.

5. Demonstrate with Conditional Probabilities
The overachieving student may wish to demonstrate this result more formally through the use of conditional probabilities.