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?
Alice and Bob are happily married, and decide to have children. Alice is proud of her long blond hair and brown eyes. Bob is also happy with his brown eyes, which he inherited from his auburn father, although his mother was green - eyed.
Alice knows that there is a small chance she might have a daughter looking like her (Alice's) mother, and that her daughter is much more likely to look like her. Bob, on the other hand, believes he won't have a son who reminds him (completely) of his father.
1. Can you determine the colour of Bob's hair?
2. Can you describe the eye colour of both Alice's parents?
3. How likely is it that Alice and Bob will have a blond son with green eyes?
4. How likely is it that they will have an auburn daughter?