There are 4 balls, two red and the two blue. You choose a color each time and a random ball is picked from the sample (w/o replacement). If your choice and the random pick matches, you gain one dollar. Repeat this four times. How much would you pay to play this game
If you could play a game just once with two choices: take $1 or have a 1/10 chance of getting $10, what would you choose? How about $1 vs 1/10 chance of $15? How about $10000 vs 1/10 chance of $100k?
there are 100 bags, each contains 100 iron bars except one that contain 100 gold bars. give you a scale, how to identify the special bag by weighting only one time?
100 pennies in a jar. 1 penny has 'heads' on both sides. You pick a penny out of the jar and give it to your friend (without looking at the penny). Your friend flips the penny in the air and gets 7 heads in a row. Which penny do you have? Why?
I have 100 coins, 99 that are heads/tails and one that is double sided heads. If I pick one of the coins at random, flip it seven times, and get 7 heads in a row, is the coin more likely to be double sided heads or a regular heads/tails coin.
19x19
'how much do you want to bet on a dice game where you can reroll if you don't like your first try?' (roughly paraphrased) = What is the expected outcome of a dice game where you can re-roll if your first roll is 1-3?
X,Y ~ Phi(0,1) (normal distribution). What is the probability that X > 5*Y
Which is bigger, 2^(1/3) or 10^(1/10)?
We are playing a game where the first person to say "40" wins, and each player must add 1-10 to the previous number. For example, I say 5; you can say any number 6-15 to which I have to react. For you to say "40" first, what is your strategy? Hint: You need to choose whether or not to go first, then your strategy going forward.
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