You have a deck of 52 cards, and you keep taking pairs of cards out of the deck. if a pair of cards are both red, then you win that pair; if a pair of cards are both black, then I win that pair; if a pair of cards has one red and one black, then it's discarded. If, after going through the whole deck, you have more pairs than I do, then you win $1, and if I have more pairs than you do, I win $1. What is the value of this game in the long run?
Suppose N students participate in a coin flip experiment, when they get heads they stop, when they get tails they keep going. All students will stop after the second trial no matter the results. Y is the binary indicator of whether they claim they cheated in the experiment. Estimate how many students cheat in this experiment.
Interesting question: From a deck of 52 cards pick 26 at random. From this set of 26 you pick two cards. You win if the both of these cards are of the same color. Is this a game you would prefer over one in which you win by picking two (first two picks) of the same color at random from a deck of 26 with equal number of black and red cards
Suppose that you have a fair coin. You start with $0. You win 1$ each time you get a head and loose $1 each time you get tails. Calculate the probability of getting $2 without getting below $0 at any time.
toss 100 coins, what is the probability of getting more than 60 heads?
There are two racks, X and Y. X contains red (R) socks with probability 0.4 and black (B) socks with probability 0.6. Y contains R with probability 0.7 and B with probability 0.3. I pick a rack randomly. From that rack, I pick 2R. What is the probability that those 2R come from rack X?
How to calculate row product of a matrix, use a language you're familiar with.
There are two agents A and B. A has 'n' coins and B has 'n-1' coins (n>1). If they toss all the coins, what is the probability that B gets more heads than A (gets heads)?
The price of a stock is $10 now. It has .6 prob. increasing to 12 and .4 prob. going down to 8. Interest rate is 0. What's the value of a call option with strike $10?
From (0,0,0) to (3,3,3) in 3D space how many paths are there if we move only right, forward or up?
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