A man went to Monte Carlo to try and make his fortune. Whilst he
was there he had an opportunity to bet on the outcome of rolling
dice. He was offered the same odds for each of the following
outcomes: At least 1 six with 6 dice. At least 2 sixes with 12
dice. At least 3 sixes with 18 dice.
Two bags contain different numbers of red and blue marbles. A marble is removed from one of the bags. The marble is blue. What is the probability that it was removed from bag A?
You and I play a game involving successive throws of a fair coin.
Suppose I pick HH and you pick TH. The coin is thrown repeatedly
until we see either two heads in a row (I win) or a tail followed
by a head (you win). What is the probability that you win?
Four cards (two cards with 1 and two with 2) are shuffled and
placed into two piles of two
You have two trays labelled 1 and 2.
Starting with the first pile of cards - turn a card over:
You win if all your cards end up in the trays
before you run out of cards in one pile.
You lose if there are cards left in a pile that
you cannot reach.
What is the probability that you win?
What happens if you have six cards in the two piles (three with
one and three with 2)?
Do your odds increase or decrease?
Can you see any patterns in successful and unsuccessful
placement of cards in the piles?