Three family members with same birthday - what are the odds?
By Simon Singh
Posted on July 12th 2021
The Sun reported a story last year of a baby, mother, and grandmother who all shared the same birthday, the 8th Feb. Isn’t that lovely! Furthermore, the headline suggests they beat odds of 50 million to one to achieve this feat. Hmm, sounds fishy to me - let's do some investigation.
Some basic math(s)
We all know there’s 365 days in a year, or more precisely 365 and a quarter. We’re pretty sure The Sun wouldn’t be anything less than accurate, so let’s try and see how they’ve got their 50 million to 1 figure. Lets assume they multiplied 365.25 three times.
365.25 days x 365.25 days x 365.25 days = 48.72M
Well, that is pretty close. 48.72M to 1 just isn’t as catchy - we’ll grant them some artistic license.
Indeed, according to the article a William Hill representative agreed, stating:
"We would put the odds in the region of 50 million to one for three generations of the same family sharing a birthday."
Is it that remarkable?
The problem with this calculation is that it makes a large assumption. Nobody specified which day the grandmother was to be born on, so the chances of her being born on her birthday are a rather less exciting 1 to 1, or 100%. Therefore the calculation becomes:
1 x 365.25 days x 365.25 days = 133,407
This produces a rather less exciting figure of 133K to 1.
Hey, that’s still pretty high odds
The story does show an image of the granddaughter Evie with her SISTER Georgia. There’s no mention of Georgia having the same birthday as the mum, so presumably she hasn’t. So it’s not just a single grandmother, mother, granddaughter situation? How does that impact the odds?
The more children in the family, the more likely this is to happen. Let’s look at an example:
Imagine the grandmother had five children, who all went on to have five children each. How would that affect the odds?
The odds of at least one of the five children being born on her birthday would drop to:
356.25 / 5 = 73
And the odds of at least one of the twenty-five grandchildren being born on her birthday would drop to:
365.25 / 25 = 14.61
Making the new calculation:
73 x 14.61 = 1066
That’s just over a thousand to one. But without knowing how many children are in the family, it’s impossible to work out what the real odds are. It’s certainly much lower than the 50 million to 1 nonsense in the headline.
Conclusion
In this non-story, the odds have been badly calculated and don’t resemble the real odds of such an event happening. Realistically, the chances of a grandchild being born the same day as her mother and grandmother would probably be less than 365. The following are factors:
- Number of children in the family
- Likelihood of mother attempting to reach the "feat" once she's got same birthday as her mother.
- Family events 9 months prior to 8th February than may encourage sexual activity.
Always take such sensational stories with a pinch of salt. I was pretty excited to read about the 50 million to 1 odds, but have been left feeling deflated. The Sun has let me down, what a surprise!