Trace: • winter2014
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Table of Contents
The Fox and the Rabbit
In the forest, there is a meadow. A fox and a rabbit each take 10 seconds to cross this meadow. One day, they both cross this meadow. Their arrival time is uniformly distributed from 4:00 to 4:01 pm. If the fox and the rabbit happen to be in the meadow at the same time, the fox will eat the rabbit. What is the probability that the rabbit survives?1)
Black and White Hats
In a box, there are 3 black hats and 2 white hats. Tom, Bob and Bill each take a hat from the box and place it on their head without looking. They are lined up with Tom at the back, and Bill at the front (so Tom can see Bob and Bill, Bob can see Bill, but Bill can't see anyone). They cannot see their own hat. They are each asked if they know what color hat they are wearing. Tom says he doesn't know, Bob also says he doesn't know, but Bill says that he does know what color his hat is. How does he know, and what color is his hat? 2)
Trains and a Fly
Two trains are traveling toward each other. Both are traveling at 50 km/h. When they are exactly 200 km apart, a fly starts traveling from one train to the front of the other. Once he gets there, he turns around and travels back to the first train. He continues until the trains meet. How far is the fly's total travel distance? 3)