Three fair coins are tossed in the air and they land with heads up. Can you calculate the chances that when they are tossed again, two coins will again land with heads up?
You are offered an opportunity to win a fortune. There are 100 precious black stones and 100 unworthy white stones. There are two different sacks labelled as "Heads" and "Tails". You can distribute the stones as you wish. Then a coin will be flipped. Then you will have to choose a stone from the corresponding sack. If you pick up a black stone, all the fortune of black stones is yours but if you pick up white, you get nothing.
How will you distribute the stones so that you can maximize your chances of winning?