You begin with $100. You flip a fair coin. Heads, you get 1$. Tails, your money gets inversed (i.e. first tails, your money is now 1/100). What is the expected value after 7 flips? (hint: recursion)
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In a pack of cards what is the expected number of cards one has to draw to get get cards of all four suites.
What is the expected value to you of the following game: You and another person have 3 coins each. You both flip all of your coins and if your three coins show the same number of tails as the other person, you pay them $2, otherwise they pay you $1.
What the probability of getting 2 consecutive heads in a total of N tosses (I found this one pretty hard and I didn't figure out the right answer at the time.)
king's party, ten servants bring 1000 bottles of coke each. One servant brings pepsi which is a different weight then coke. Fiqure out the pepsi servant with one weighing on a standard scale
We play a game. You flip two coins, if you get both heads I give you $1. If you get both tails you flip again. If you get one of each, I pay you nothing. What's the expected value of this game?
If I had 4 coins and I flipped them and you get paid $1 for every head, what is the expectation of earnings? If I then said you had a magic wand and you could use it to tap on an even number of coins to flip them again, what would your expectation of earnings be? (i.e. you could either flip 2 or 4 coins).
If you have one hundred coins, at least one fair and at least one not fair, is the chance that you will get an even number of heads sometimes 1/2, always 1/2, or never 1/2?
How many ways can you arange five people at a round table, such that there they are in increasing age order (clockwise or anti-clockwise)?
Roll a fair dice, if it's a prime number, you pay me that number times $100, if it's not a prime number, I pay you that number times $100. Consider 1 as a prime number. How much willing to pay to play this game.
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