Suppose you are given a cube, you break the cube in 3X3X3 pieces. However, before doing so, all 6 faces of the cube were colored green. All the other faces not colored green will be white after breaking it up. You randomly pick a small cube and see one face which is green. What is the probability that the cube is an edge cube?
You have a fair penny. It takes a dollar to play and to win, you must flip 4 heads in a row for 10 dollars. Should you play?
You have a total of 4 investments to make of 100 dollars. You can either invest in a stock which if it goes up in value, you gain an additional 100 dollars, if it goes down, you lose 50 dollars. Or you can bet on whether the stock will go up or down at the casino, where you either win 100 if you're right or lose everything if not. Can you devise a strategy where you will always make a profit?
A game where two players each throw two dice each. If any one die matches the other, you win a dollar. If there is no match, you lose a dollar. Would you play this game or not and why?
1. How do you simulate stock price with VBA? 2. Std.=? 3. VaR=? 4. Three doors, it takes you 1 minute to go through the first door, it also takes you 1 minute to go through the second door, it make your speed slow down 1/2 after going through third door. Only the first door is the right way to go out. You choose each door with the equal probability. How much time will you go out in expectation? 5. You have n 1-meter long ropes, and you could connect two nodes together n-1 times. What is the probability for you to finally get a whole n-meter long rope without rings?
1a) A bus runs on a loop. It takes to the bus 10min to complete the loop. You go to the bus stop at random times, what's the expected time you'll be waiting for the bus? 1b) Along the way the bus driver stops for 10 min with a 50% chance. For how long you wait now? 2) There's a rounded table, you wanna place three legs randomly, what's the chance the table stands?
Expected length of the longest segment of a unit-length stick broken in 2 places.
What's your biggest weakness?
What is the probability that three random points on a unit circle would form a triangle that includes the center of the unit circle?
what will you do if your manager asks you do something which you think is wrong?
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