Lumos

Question: A photon starts moving in the random direction from the center of the square of size 3. Let’s say it first colloids to the glass wall AB. What is the expected distance traveled by the photon before hitting the wall AB again? . . C A P T A I N I N T... Continue Reading →

 Misogynist country

Question: In a country in which people only want boys, every family continues to have children until they have a boy. If they have a girl, they have another child. If they have a boy, they stop. What is the proportion of boys to girls in the country? . . C A P T A... Continue Reading →

Bias and Unbias

Question: Robin and Williams are playing a game. An unbiased coin is tossed repeatedly. Robin wins as soon as the sequence of tosses HHT appears. Williams wins as soon as the sequence of tosses HTH appears. The game ends when one of them wins. What are the probabilities of winning for each player? . .... Continue Reading →

Life and luck

Question: You and your friend are caught by gangsters and made to play a game to determine if you should live or die. The game is simple. There is a deck of cards and you both have to choose a card. You can look at each other’s cards but not at the card you have chosen.... Continue Reading →

Chameleons go on a date

Question: On an island live 13 purple, 15 yellow and 17 maroon chameleons. When two chameleons of different colors meet, they both change into the third color. Is there a sequence of pairwise meetings after which all chameleons have the same color? . . C A P T A I N I N T E... Continue Reading →

All men must die

Question: One day, an alien comes to Earth. Every day, each alien does one of four things, each with equal probability to: (i) Kill himself (ii) Do nothing (iii) Split himself into two aliens (while killing himself) (iv) split himself into three aliens (while killing himself) What is the probability that the alien species eventually dies out... Continue Reading →

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