UKC

In 2014, 695,233 babies were born in England and Wales. 6,649 of these were called Oliver.

If I had named my child Oliver, what is the chance that in his class at school, there would be another child called Oliver.

We could assume 30 children in his class (or less?). Name any other assumptions.
Any attempts to correct for region or socioeconomic background would be applauded.

In reply to Dan Arkle:

I made it about 1 in 10.

In reply to Dan Arkle:

If your child was born in 2014, he won't be going to school til 2018 or 2019.

In reply to Dan Arkle:

1/1 if you send him to a posh private, 0 chance if you send him to a suburban free school.

In reply to Dan Arkle:

Your child's name is actually irrelevant. For a class of 30 the question is... what are the odds of at least one Oliver in the other 29?

With the odds for any individual child (ignoring sociology) at 6,649/695,233 we flip the question around as usual and get the odds of *no* other Olivers in the class = (1 - 6,649/695,233) ^ 29 = 0.75678.

So the chance of *at least one* other Oliver is about 24.3%.

In reply to elliptic:

D'oh !! I'll get my coat.

In reply to elliptic:


That's incorrect because the probabilities of each child not being called Oliver are not independent. if the 1st is not called Oliver, the probability of the 2nd not being called Oliver is 1- 6649/695232 etc. But it won't make much difference to the answer because 30 is small compared with 696233.

In reply to Robert Durran:

Fair point. As you say though it's a tiny correction and the result is actually still 0.75678

In reply to Robert Durran:
BUT... if your child is called Oliver you need to knock one off the 6649 - there are only 6648 other Olivers.

In reply to Andy Hardy:

Eh? So at the same time as all the other kids called Ollie or otherwise born in 2014?

In reply to Dan Arkle:
6,648:695,323

The probability of your son being in his own class is 1.

So it's simply the probability of there being another boy in his class named Oliver.

Although it's probably even tricker as school years don't go from Jan-Dec so we need more information.

In reply to Dan Arkle:
Near enough 1% of kids are called Oliver.
Assume there are 14 boys other than your Oliver and none of the girls are called Oliver.
Roughly 14% chance there is another Oliver

1-.99^14 is near enough the same number, 13%.

In reply to ianstevens:


True. Though this also makes virtually no difference to the answer.

In reply to elsewhere:




No. The total number of children was given, not the total number of boys, so roughly 2% of boys called Oliver, so roughly 28% chance of another Oliver (which is in line with calculated answer).

In reply to Robert Durran:

Good point!

In reply to elliptic:


Although half the children on average a girls, and not many girls are called Oliver!

So you're looking at ~ (1-6000/600000)**(29/2) = (1-.01)**14.5 which approximately equals 1-14.5*.01 ~= .85 for no more Olivers.

Or using the actual numbers and ignoring Robert's minor correction gives 0.8699; not really worth the effort of retreating to a calculator for the difference!

So about a 13% chance of one or more Olivers. Lots of variation with small number statistics on the gender ratio.

Edit: Beaten to it by Elsewhere.

In reply to wintertree:


And beaten to the same error too!

In reply to Robert Durran:


Oh yes. So the actual calculation is closer to (1-6649/347616)^14.5 = 0.7557 giving about a 25% chance of another Oliver!

As ever a test of reading ability and not maths!

In reply to Mr Lopez:

I don't know why you are getting dislikes. Dan asked for socioeconomic considerations, and I doubt your estimates are too far off.

In reply to wintertree:


Likewise my error earlier!

In reply to Dan Arkle:
Depends on the month they were born if first year at school. I was born in August but didn't start school till Feb, 4.5 years later. I was in a class with people of the same name born in a previous year.

In reply to Lion Bakes:

Names are also fashionable. So higher densities in similar age individuals, not a random distribution. There must be a correction factor...

In reply to Kevster:


Isn't that covered by the fact we are just considering babies born in 2014?

In reply to Dan Arkle:

Nope as kids born in different years will also be in his class.

In reply to Lion Bakes:


It's good enough as a sample of names used at the relevant time.

In reply to Dan Arkle:
1 in 2 ?

Either there will be or there won't.

I remember a probability question from school. A certain number of boys, a certain number of girls and a certain number of seats on the bus. What is the probability that Jonny will be seated next to Jenny.

None I told the teacher. Jonny will be at the back with his mates, firing chewed up pieces of paper at Jenny through a biro tube!

In reply to Dan Arkle:


is there a formula for calculating the probability of someone becoming good at maths, taking into account age etc?

Or will it end up as a constant past a certain point?