Probably maybe: Ice cream variation

ice cream cones

The saying goes that “probabilities are counter-intuitive”. A simple problem might appear to have a straightforward answer at first glance, but only do we later learn, through careful explanation, that our intuition has been subverted. Indeed, human intuition is rarely to be trusted when it comes to making probabilistic judgments, especially under time pressure. Even those trained in statistics, like most readers of Significance, can fall prey to cognitive biases when making snap decisions.

But probabilities do not only manifest as paradoxes. Sometimes we can be intuitively right about a problem presented to us, albeit for the wrong reasons, or for reasons that are hard to comprehend. And sometimes we are faced with probabilistic problems for which intuition abandons us altogether.

Thus, this column sets out to put you – the reader – to the test. Each time we present a question to challenge your probabilistic instinct, along with the answer and some commentary and explanation.

So, to begin:

The problem
In the village of Chedrok, there are two ice cream sellers, Dimitrius and Zaza. Dimitrius is a hard worker. He sets up his counter every day early in the afternoon and doesn’t stop until early next morning. He serves around 220 customers per day. Zaza is more laid back. He works only a few hours in the evening and rarely at night. He serves around 45 customers per day.

Sourcing ice cream is tough in this area, so they only sell one scoop to each customer and they've both settled for just two flavors, ginger and raspberry, which are the locals’ favourites. Overall, about 50% of the customers choose raspberry. However, the exact percentage varies from day to day. Sometimes it’s higher than 50%, sometimes lower.

Dimitrius and Zaza have had a small wager going on between them. For a period of three months, each recorded the days on which more than 60% of his customers chose ginger. We’ll call such a day a "ginger day".

Who do you think recorded more ginger days?

(a) Dimitrius

(b) Zaza

(c) About the same (within 5% of each seller’s total)

Read the description again and give yourself just a minute to decide on an answer.

About the authors

Christoforos Anagnostopoulos, honorary staff at Imperial College, and Spiros Doxiadis, an entrepreneur and amateur probabilist, together created the board game Borel. The game uses probabilistic quizzes and instruments of chance – such as multi-sided dice and pouches with colored balls – to challenge players’ probabilistic judgement.