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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