Both David Spiegelhalter & Nigel Hawkes have challenged the Sun newspapers estimate that the odds of a couple having three singleton children all born at the same minute of day (as measured by the 12-hour clock) is over 300 million to 1. Each says that the answer is more like half a million to one.
I have no quarrel with their estimate as such, but questions like this do show that it really all does depend on where you stand in space & time.
Before going any further I should point out what I think is an error in David Spiegelhalter’s estimate that we could expect such a coincidence about once every three years, based on the ‘fact’ that there are about 167,000 third births a year in the UK.
The latest figures I can find (Table 4.1 Birth Statistics 2008) show that there are about 50,000-60,000 third births a year within marriage in England & Wales, which would make the true frequency about once a decade.