Guiding Financial Engineers From All Around The World

1. Consider the game in which Player A throws a fair die once. Player A receives $10 for each dot on the upturned side. How much should you set the price to play this game?

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2. You have two empty jars, 50 black marbles and 50 white marbles. If you can place any of the marbles in both jars, how can you maximize the probability of drawing a white marble?

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3. Consider the game in which there are 3 doors. Behind one of the doors is treasure chest full of gold, and nothing behind the other two doors. You must guess the door that contains the treasure chest of gold. Once you choose a door, one of the other 2 doors will open to reveal that it is empty. At that point, you may switch your choice of door to the other door that was not revealed as the empty one.

You choose Door 1. At this moment, Door 3 opens to reveal that the treasure chest is not behind this door. Hence, you know that the treasure chest lies either behind Door 1 or Door 2. Should you switch your selection from Door 1 to Door 2?

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4. Your name is Mr. 10. You are standing in a field with 2 opponents – Mr. 30 and Mr. 60. Each of you has a gun and plenty of ammunition. Each of you in in clear sight of the others and well within firing range. The goal is to maximize the probability of survival.

If you shoot at one of your opponents, you have a 10% chance of killing him. Mr. 30 has a 30% chance of killing whomever he shoots at. Mr. 60 has a 60% chance of killing whomever he shoots at. You take turns shooting in an pre-agreed to order. You shoot first, followed by Mr. 30 and finally Mr. 60. The 3 of you go through this order until one person is still standing. Who do you shoot at first?

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5. Your basketball team is down 2 points in the State Championship with possession of the ball. There’s only enough time to take one shot. As the best player on your team, your coach has designated you to take the last shot. You can go for the 2 or 3. You are a 40% shooter from 3-point range and a 70% shooter from inside the arc. If you go for the 2 and make it, the game will go into overtime where your team has a 50% chance of winning. If you go for the 3 and make it, your team wins the state championship. What shot should you take?

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6. You are playing a game with four shuffled cards. These cards are placed face down on a table. The hidden faces contain the images of clubs, spades, diamonds and hearts. You must turn over the cards one at a time until you win or lose. you win if you turnover the spade or the diamond. You lose if you turnover hearts. What is the probability that you win?

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7. Two games are offered to you. In game 1, you roll a die once and win $1 million times the number that you rolled. In game 2, you roll a die 1 million times and are paid $1 time the number you rolled after each roll. As a risk averse person, which game do you prefer?

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8. You are presented with a treasure chest that contains 999 fair quarters and 1 two-headed quarter. You pick one quarter from the treasure chest, flip it 100 times and get all heads. What is the probability that you chose the two-headed quarter?

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9. What is the standard deviation of (3, 4, 5, 6, 7)?

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10. There is a fair roulette wheel at the Bellagio in Las Vegas. This roulette wheel has only six section. One of the sections pays $6 and the other five sections pay out $1. If the cost is $1.25 per spin, should you play this game?

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