Numbers

WHAT is the risk that you are related to Baroness Thatcher? Last week a genealogist demonstrated that John Major and Margaret Thatcher are fifth cousins once removed. Should this surprise us? Or is it just that we're all related if you trace the branches far enough?

John Major's great great great great great grandfather, one John Crust, husbandman of Leake, was Margaret Thatcher's great great great great grandfather. Those seven generations of one family and six of the other take us back to the early 18th century. The population of England and Wales was then around 6 million, of whom about 100 would have been direct antecedents of John Major. (The theoretical maximum of 128 five- times-great grandparents could be diminished by marriage of relatives.) Comparing Major's hundred with Thatcher's hundred, what are the chances they have someone in common?

The underlying mathematical question is that of taking two random samples of 100 items from a collection of 6 million. The odds work out at around 500 to 1 against their having a common member. On that basis, over a thousand readers of this newspaper could be sixth cousins of Lady Thatcher.

Small samples from large populations can easily produce apparently unlikely coincidences. After all, it takes only 23 people in a room to have a greater than even chance of two having the same birthday. It has also been calculated that any cup of tea you drink is odds-on to contain an atom that was once part of Julius Caesar's urine. A chance relationship to Lady Thatcher cannot be worse.