On the TV show Deal or No Deal they often refer to a player having the same amount of money in their box as the previous day.
There are 22 players on each program who all have a different amount of money in their box from the other 21 players. On each program there is always one new player who was not on the previous day's program.
So what is the probability that at least one player on a program has the same amount of money as the previous day?
The probability of a single player NOT having the same amount of money as the previous day is 21/22.
The probability of none of the 21 returning players having the same amount of money is 21/22 raised to the power of 21 - that is, multiplied together 21 times.
That works out at about 0.376, so the probability of at least one player having the same amount of money is 1 - 0.376, or 0.623.
This is almost 66% or two-thirds, so statistically at least one player will have the same amount of money as the previous day on almost two programs in every three!