I have two envelopes, and inside each I have put some money. In fact, one envelope contains twice as much...
Continue reading...probability
Rising Sequences in Card Shuffling
In Seven Shuffles we saw that it takes about 7 random riffle shuffles to randomize a deck of 52 cards. This means...
Continue reading...Perfect Shuffles
We know from the Fun Fact Seven Shuffles that 7 random riffle shuffles are enough to make almost every configuration equally likely...
Continue reading...Buffon Needle Problem
A plane is ruled with parallel lines 1 cm apart. A needle of length 1 cm is dropped randomly on...
Continue reading...Drunken Walker and Fly
Imagine a drunken person wandering on the number line who starts at 0, and then moves left or right (+/-1)...
Continue reading...Making History by Card Shuffling
Did you know that whenever you shuffle a deck of cards, it is quite likely that you are making history?...
Continue reading...Birthday Problem
How many people do you need in a group to ensure at least a 50 percent probability that 2 people...
Continue reading...Are Coins Fair?
When you flip a coin, what are the chances that it comes up heads? If the coin is “fair” then we...
Continue reading...Matching Problem
Suppose I return N homeworks randomly to my N students. What is the chance that no student gets back her...
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