Danny Baker’s Sausage Sandwich game is often a great radio platform for exercising your statistical intuition in real-time.

If you know it, Danny asks as celebrity sportsperson three fairly trivial questions about fairly inconsequential aspects of their day-to-day lives, and to which only they can know the answer.

Each question takes the form of a three-way multiple-choice question, and two contestants get to select in advance which answer they think the celeb will give.

As an example, the final question takes the form: “I offer you a sausage sandwich. Do you have red sauce, brown sauce, or no sauce at all.”

If the contestant guesses the celeb’s answer correctly they score a goal (ostensibly the same as scoring a point, but it’s definitely not that).

You can see the scope for the application of statistical knowhow straightaway. And that particular question often raises the questions of north-south sauce preference, and the likelihood of anyone wanting no sauce at all on a sausage sandwich.

More often that not, to work out an optimal answer you’d need to source some distribution data on the average number of televisions per household, or UK house number distributions – but today’s question 2 was straight out of a Probability 101 class.

Danny invented the question on-the-fly for today’s celebrity climber Molly Thompson Smith, and which took the following form:

If you take the last digit of your phone number, and the last digit of your friend Jack’s phone number, and multiply them together. Do you get:

  • A number between 0 and 12
  • A number between 14 and 24
  • A number greater than 24

Which is a fantastic little mathematical problem in itself. And one which I completely failed to intuit in real-time. I managed to correctly rule out the middle option as the least likely, but without running through the maths in my head I plumped for the third.

Here’s a distribution of all the possible answers:

And, assuming that last digits of British phone numbers are indeed evenly distributed, here are the actual probabilities:

i.e. “0 to 12 was clearly the optimal response for a contestant to give.

And the big reveal… if you’re playing along at home … Molly’s actual answer was “between 14 and 24“.

Danny Baker 1 – Maths 0