There are 1000 buckets, one of them contains poison, the rest are filled with water. They all look the same. If a pig drinks that poison it will die within in 30 mins. What is the minimum amount of pigs you need to figure out which bucket contains the poison.
You are playing a game where the player gets to draw the number 1-100 out of hat, replace and redraw as many times as they want, with their final number being how many dollars they win from the game. Each "redraw" costs an extra $1. How much would you charge someone to play this game?
I have 10 cards face-down numbered 1 through 10. We play a game in which you choose a card and I give you the corresponding dollar amount. a) What is the fair price of this game? b) Now, after picking a card you can either take the dollar value on the card or $3.50. Also, cards worth less than 5 are now valued at $0. What is the maximum price you are now willing to pay for the game?
What's the square root of 2000?
Say I take a rubber band and randomly cut it into three pieces. What's the probability that one of the pieces has length greater than 1/2 of the original circumference of the rubber band.
The dice game mentioned above: You roll a 100-sided die. You can choose to accept the value of this roll for $x, where x is the value showing. You can choose to re-roll the die for $1. What is the strategy you employ and what is the fair value of the game?
You have three barrels. One barrel is filled with apples, one with oranges, and one with both apples and oranges. Each barrel is mislabeled. You can take out as many fruit as you like form each barrel and look at it. What is the minimum number of fruits you need to remove to correctly label the barrels?
Game1 : a dice roll with a 100-faces dice, labeled from 1 to 100. 1. You get to roll once and receive the amount of dollars labeled on the face, how much would you like to pay for this roll. 2. How much would you pay if you can roll the dice twice if you are unsatisfied with the first outcome? 3. You can roll the dice infinite times, and costs 1 dollar for each roll except the first one. What is your strategy? Game2: you are competing in a game with 2 other players. with a 21-faces dice (labeled 1-21). All three of you gets to choose a number and then roll the dice. Whoever chose the number closest to the outcome wins. What is your strategy? another twist: what if all three of you can communicated?
Flip a coin. if head, I win 1 point. If tail, u win 1 point. The person who first wins 2 points wins the game. And the loser must pay winner $1. However, if I have a option which I can increase the stake of the game to $2/game, what is the value of such option.
I have 20% chance to have cavity gene. If I do have the gene, there is 51% chance that I will have at least one cavity over 1 year. If I don’t have the gene, there is 19% chance that I will have at least one cavity over 1 year. Given that I have a cavity in 6 months, what’s the probability that I have at least a cavity over 1 year?
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