Coincidence odds are wrong yet again

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The Sun today features a story about a family who have had three children all born at 7.43 (two am and one pm). Heartwarming, but the quoted odds of 300,000,000 to one are sadly wrong.

They presumably calculated that there are 60 x 12 = 720 times that could be recorded to the nearest minute (ignoring am or pm). Then they multiplied this up 3 times to get 720 x 720 x 720 = 373,248,000.

But we want the probability of all three being born in the same minute, not of them all being born at 7.43. So the first birth does not contribute to the coincidence - it just sets the 'target' for the other births. So the correct answer is 720 x 720 = 518,400 (even making the probably inappropriate assumption that births are uniformly distributed through the day). And since around 167,000 third children are born in the UK each year, we would expect this event to happen around on average once every three years. So remarkable for the Rigby family, but not that remarkable to hear about.

The Daily Mail made the same mistake recently with the recurring story of three children being born on the same day.

We've got a lot more on coincidences here, although it does make us seem a bit miserable, continually puncturing the grand odds being quoted.

(Thanks to Jack Boericke for pointing out this story)

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I'd wonder whether the medical staff present at the third delivery knew of the coincidence of the first two children- if they did, it would raise the possibility of the third time-of-birth being "fudged" if it was close to 7:43- what stage of the process do they count for time-of-birth anyway? Would lower the odds even further.

Spotted that one this morning. Now try calculating this one. Numerous problems, although by any standards it's unlikely.

Did you see that the Guardian managed to inflate the very same probability 1000-fold?