Let's play a game - I give you a 12 sided die and will pay you whatever the die lands on. If you are unhappy with the roll, you can choose to roll another two 6-sided dice and I wil pay you the sum of the two dice. How much are you willing to pay to play this game.
We consider numbers from 1 to 1 million. How many digits 2 are there??
If I write down all of the numbers from 1 to 1,000,000 on a page, how many times do I write down the digit 2?
Imagine I flip 100 coins in a sequence, and you need to guess the sequence. You are allowed to ask one yes/no question. What do you ask to maximize the probability of guessing the sequence?
You have a dart board thats split in half. If you hit the left half, you get 2 points, if you hit the right half, you get 3 points. If you have an 80% chance of hitting the dart board on any given throw and a 70% chance of hitting the side you're aiming for (given that you hit the dartboard so a 30% chance you hit the side you aren't aiming for), if you have an unlimited number of throws, what's the probability you get a score of exactly 7
Two dice - one 10 sided one 6 sided. Guess the roll of the two dice, no penalty for guessing under. You receive the amount on the dice if you guess it. What is the expected value? What is the bet that would maximize your payout?
The only difficult question I was asked went as follows: "You and your opponent flip a coin. If the first player gets heads, the second player pays him $30. If he flips tails, the coin goes to the second player. If the second player flips heads, he wins $30 from the first player. How much should you pay to go first?"
Two people painting a house, one on his own takes 1hr and the other takes 2hrs, how long does it take for both to paint the house. After my answer he asked how confident I was then said that I could bet on my answers, £1 if I got it right, -£1000 if I got it wrong - should I take the bet.
100 coins in a circle, clockwise labeled 1-100. Starting at coin 1, you flip each one moving clockwise. If a coin lands tails, you keep it, if it lands heads, you remove it. After a long time, only one coin will remain. What would you expect its label is?
What is the expected value of rolling two dice?
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