You have a standard deck of 52 cards. I draw a card and tell you I drew hearts. Now you draw a card from the cards that are remaining. What is the probability that you will also draw a heart? Again, you have a standard deck of 52 cards. I draw 13 cards and tell you I drew exactly 5 hearts. Now you draw 13 cards from the cards that are remaining. What is the expected number of hearts you will draw?
sum of all odd numbers between 1 and 100.
3. There are 30 blue and 30 red balls and two urns. You play a game. Your opponent has the right to arrange the balls in the two urns as he pleases, without telling you what he did. You then must draw a ball from an urn of your choice. You win $10 if you draw a blue ball, otherwise you get $0. How much would you be willing to pay to play this game?
How many numbers from 0 to 1000 contain at least one 2?
1.5 chicken lay 1.5 eggs in 1.5 days. How many eggs do 9 chicken lay in 9 days?
If 1st Jan 2015 was on a Monday, which day would it be on 1st Jan 2025?
Given deck of cards A and deck of cards B, which deck would you rather choose from if you need to choose two cards of the same color on consecutive draws? Deck A is a normal 52 card deck, Deck B is a 26 card deck with 50% black and 50% red. What if we add deck C, which is a 26 card deck that comes from a random subset of deck A?
P(rain on Saturday) = p1, P(rain on Sunday) = p2. What is P(rain on the weekend)?
How would you estimate pi?
A Trie problem
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