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?
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.
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?
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)
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.
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?
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