The Birthday Bet

I am working on a post about risk and decision-making and I need your help.

I am trying to get a feel for the risk numeracy of the average doctor – I realise that none of my readers is “average” but please take the time to read the following scenario and give me an honest answer.  Please try to avoid Googling the “right” answer – I am after your gut feeling.  I want to know if this were you – and you had to take a guess what would you say?  It is not about the maths – it is about how doctors think…  yes I am data mining your brains.  Sorry.  That is the sort of thing I do for fun on nights here in Broome!

OK here is the scenario;

You are invited to the Hospital Xmas Party by a nice young nurse.  Unfortunately they tell you the wrong time – so you turn up in you fancy dress Chicken Suit an hour early.  Not sure what to do – you decide to engage in idle banter with the Hospital Tea Lady who is carefully arranging her sausage rolls on a long table.  After 5 minutes you discover that you both lived on the same street in Wagga Wagga – although she was there in the 1950s, 30 years before you were born.  Nice coincidence!.

After 20 minutes the conversation stalls a bit, and during and awkward silence she proffers the following bet:

I’ll bet you that there are two people coming tonight who share the same birth date – not necessarily the same year – but the same date eg. the 6th of May…

Of course there are 500 people coming to the party – so it is a pretty easy bet.

OK, to make it interesting.  Lets ask each person as they arrive their birthdate.  And see how long it takes before we have a match i.e.  a pair with the same Birthday.

OK – sure.  How many people do you think?  Tell me how many people need to arrive at the party before it is a better than 50:50 bet that there will be a shared birthday?  That is – when would it be in your favour to take the Tea Lady’s Bet

Thanks for putting your mathematical pride on the line.

The answer to the questions is….. *drum roll*….  23.

Yes, just 23 – this is much lower than most doctors answer when asked to give a gut feeling about the problem.  In my own offline informal torturing of friends and coworkers the usual answer is somewhere between 150 & 200 partygoers.

So how did the FOAMed crowd do on this version of the famous betting dilemma?

Here is the latest spread:

Screen Shot 2014-12-10 at 9.35.10 pm

Assuming that a heap of smart folk either knew the answer (and did not rely on intuition) or Googled the puzzle and cheated (once again – no intuition) – the correct answer was the most frequent answer.

What I was really after here was a measure of the average Docs “intuitive” risk / probability instinct for problems where the answer is calculable but there is uncertainty.

I think it is pretty likely that the average doctor went with 183 (i.e half of 365) as a best guess. There was a spread around this number if you exclude the folk who got it right.

If you want to see how the actual mathematic probability equations work – check out MATH IS FUN here

Of course if you are really into n! factorial equations then there is a 99% chance that you do not actually have 23 friends whom you might invite tot your Birthday – so its all a bit academic really!



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