As being an arse is one of my favourite pasttimes, here is a calculation on the probability of saying the same word as someone else over time.

Frequency of a common word ‘you’=5% *)

Frequency of approximately the 1000’th most common word ‘upstairs’=0.009% *)

Estimated time you are engaged in conversation/day = 1 hr

Say you interrupt someone by saying a random word.

The probability of him saying ‘you’ at the instance of interruption is 5%,

The probability of you interrupting with ‘you’ is also 5%

so the probability of you saying the same word is 5%*5% = 0.25%,

The same calculation for the word ‘upstairs’ equals = 0.00000081%

Estimated number of times you interrupt someone/hour of conversation = 10 times

So you have 10 chances per hour of conversation of interrupting someone,

This means you have somewhere between 2.5% and 0.0000081% chance of

saying the same word as someone/day.

1 year is 365 days, so the probability of saying ‘you’ at the same time

as someone else during one year is 1—((1–0.025)^365) =~ 99.9%

And the probability of saying ‘upstairs’ at the same time

as someone else during one year is 1—((1–0.000000081)^365) =~ 0.3%

If we increase the time span to 10 years the calculation becomes

1—((1–0.025)^3650) =~ 100% and

1—((1–0.000000081)^3650) =~ 3%

Saying the average person lives 70 years this equals 25550 days, so your chance

of saying one of the 1000 most common words at the same time as someone else during your lifetime is somewhere between 20% and 100%.

As RAWRxRandy and others pointed out, people talking to eachother are prone to be using the same vocabulary, so the true probability is probably in the higher portion of this range.

*) Source: Most common words in TV and movie transcripts:

http://en.wiktionary.org/wiki/Wiktionary:Frequency_lists/TV/2006/1-1000