Every person in this world (assume 7 billion people) has a fair coin except one. One person has a coin which has heads on both sides. A random person is chosen who flips his/her coin 100 times. If it comes out to be heads each time, what is the probability that the person has a fair coin?
A bag has 20 blue balls and 14 red balls. Each time you randomly take two balls out (Assume each ball in the bag has equal probability of being taken). You do not put these two balls back. Instead, if both balls have the same color, you add a blue ball to the bag; if they have different colors, you add a red color to the bag. Assume that you have an unlimited supply of blue and red balls, if you keep on repeating this process, what will be the color of the last ball left in the bag? What if the bag has 20 blue balls and 13 red balls instead?
At one point, a remote island’s population of chameleons was divided as follows:
- 13 red chameleons
- 15 green chameleons
- 17 blue chameleons
Each time two different colored chameleons would meet, they would change their color to the third one. (i.e.. If green meets red, they both change their color to blue.) Is it ever possible for all chameleons to become the same color? Why or why not?”
You have Some Terminal Condition, which necessitates taking two pills a day: one Pill A and one Pill B. If you neglect to take either pill, you die; if you take more than one A or more than one B, you die. If you don’t take them at exactly the same time, you die. [...]
N ants are randomly spread on rod 1 meter long. They can move either to the left or to the right. They move at a constant speed of 1 m/s and when they meet, they shake hands and reverse their direction. Assume that the shaking of hands involves no time delay. If an ant [...]
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