Two Interesting Math/Econs Problems

Ok, readers!! See if you are smart enough to figure out the answer to these two problems below:

1) You have just entered a gameshow where you are given the chance to win a car. There are three doors: 2 with a goat behind them and 1 with a car. You choose one of the three doors and the host opens one of the remaining two doors. It is revealed that the object behind the door that he has just opened is a goat. Now, there are two doors left. Are you going to switch? We will assume that the host knows which door contains the car.

2) There are 6 participants in a room. Three girls and three boys and they play a dating game. Their date preference table is shown below:

Women:
w1 : m1> m2> m3
w2 : m1> m3> m3
w3 : m1> m2> m3

Men:
m1 : w1> w2> w3
m2 : w1> w2> w3
m3 : w1> w3> w3

What will the outcome (aka who will end up dating whom) be if:
a) The man makes the first move
b) The woman makes the first move

What conclusion can you draw from the dating game?

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