I have 100 green marbles and 100 red marbles and I can divide them up however I want between 2 bags. There has to be 1 marble in each bag, other than that no restrictions. You do not know how I divide them up or which bag you are getting. If you pick a green marble I pay you 100 dollars, If you pick a red, I pay nothing. What is a fair price for this game?
3000 Apples to be transported from city A to city B, between which the distance is 1000 miles. When there is apple on the truck, one apple disappears as every mile driven. Assume unlimited gasoline, how many apples maximum can be transported to city B? Given your answer is x, what market would you make on a lottery: you win 10 dollars if your answer is correct, otherwise 0 dollar. (All calculation must be done without pen and paper)
probability of getting even number of heads when flipping 39 coins
What is 38 squared?
First through a dice with numbers 1 to 8. If you want you can stop or otherwise through a dice with numbers 1 to 12. You win the money equal to the final number on the face. What will be your strategy?
If there are N points on a circle, and you draw a chord between each of them, how many regions is the circle subdivided into?
Given two bowling balls and one weighs X kg, they are the same density, if this bowling ball is 10 inches diameter and the other is 16 inches diameter, how much does it weight?
there are 3 problems presented during the phone interview. the first two could be found here. I only give 3rd problem: I am thinking about two positive integers: a and b. I can tell you a/b is belong to the close interval [0.48, 0.52], then give me all the possible values for b no matter what value a takes.
A cube painted with red paint was divided into 27 smaller cubes (3*3*3). Randomly pick one and toss it. What is the probability that at least one of the sides that can be seen has paint on it.
You have two dices. There are two players. You each pick a number. The person who picks the number closest or equal to the sum of the roll of the dices is the winner. What is the strategy to optimize chances of winning. Also, is it always better to pick the number that has the highest chance of being rolled? This situation does not apply to the rules of this game. For example, this question could apply to the rules when the two numbers on the die are multiplied rather than added.
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