Our gut reactions to probability aren’t always correct

We’re not always good at doing maths quickly. Often we go by gut feeling, rather than what the numbers tell us. Take childbirth, for example; imagine a woman has given birth to three children, who are all boys. If she becomes pregnant again then people might say – because all of her current children are boys – that there is a strong chance her next child will also be a boy, or that she must be ‘due’ a girl next. And yet biology tells us there is still a 50 per cent (or 1:1) chance of her having a boy because each conception is an independent event and is unaﬀected by the existence of her previous children.

The same is true of coin tosses. Just because a coin comes up heads ten times in a row, a head is no more likely than a tail on the 11th ﬂip (provided the coin is not ﬁxed). The probability of having a boy, or the coin coming down heads, are both 1/2, no matter what’s happened previously. The situation is different if the events are dependent – if you pull an ace from a pack of cards without returning it, the probability of picking another ace goes down from 4/52 to 3/51.

This is especially true when unlikely events occur. Take natural disasters, for example. It is often said that events like ﬂoods, tsunamis and hurricanes are ‘once every 100 years events’, and people are surprised when they occur more often. What it actually means is there is a 1 per cent (1 in 100) chance of the event happening in any given year. Again, however, these are independent events: if a ‘once in 100 years’ ﬂood happened last year, that doesn‘t mean that it can’t happen again this year. It is unlikely – but unlikely things happen all the time.