IEOR 4106: Introduction to Operations Research: Stochastic Models Professor Whitt Sample Entertainment The following problems may seem frivolous, featherbrained, foolish, fanciful, fatuous or all of the above, but if you understand them, you may be able to approach the world with a better understanding of randomness and uncertainty. 1. The Game Show Suppose you are on a game show, and you are given the choice of three doors. You win what is behind the door you choose. Behind one door is a new car; behind the other two doors are goats. You pick a door, say door number 1. Afterwards, the game show host, who knows what is behind all the doors, opens another door, say door number 3, and shows you a goat. He says to you, “Do you want to change your pick to door number 2?” Is it to your advantage to switch your choice of doors? Why? 2. Cars and Trucks Three out of every four trucks on the road are followed by a car, while only one out of every ﬁve cars is followed by a truck. What proportion of vehicles on the road are trucks?
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