Peter throws two darts at a dartboard, aiming for the centre. The second dart lands farther from the centre than the first. If Peter now throws another dart at the board, aiming for the centre, what is the probability that this third throw is also worse (i.e., farther from the centre) than his first? Assume Peter's skillfulness is constant.
Answer: Since the three darts are thrown independently, they each have a 1/3 chance of being the best throw. As long as the third dart is not the best throw, it will be worse than the first dart. Therefore the answer is 2/3.
I have a triangular table which has sides of 20, 25 and 50 inches.
What is the area of the table?
Hint: Try drawing a scale version.
This triangle can not exist. The longest side is longer than the sum of the other two.
I once cashed a cheque at the bank. I had spent £0.05 before I realised the bank clerk had made a mistake. He had transposed the pounds with the pence. I now had exactly twice the value of the original cheque. What was the original cheque's value?
At a movie theatre, the manager announces that they will give a free ticket to the first person in line whose birthday is the same as someone who has already bought a ticket. You have the option of getting in line at any time. Assuming that you don't know anyone else's birthday and that birthdays are distributed randomly throughout the year, what position in line gives you the greatest chance of being the first duplicate birthday?
Hint: This is a very difficult puzzle.
The solution requires quite a lot of knowledge of probability and is beyond the scope of a simple solution.