Will it be a rollover?

As of the 23rd May 2022 this website is archived and will receive no further updates.

understandinguncertainty.org was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

Many of the animations were produced using Flash and will no longer work.

Suppose there are $aN$ lottery tickets sold, each with a chance $1/N$ of winning.

Then each has a chance $1 - 1/N$ of losing, and the chance that they all lose is
$$\left(1-\frac{1}{N}\right)^{Na} \approx e^{-a},$$
where $e=2.718$ is the base of natural logarithms, and is also the limit of $(1 + 1/x)^x$ as $x$ gets large. For $a = 1,2,3,4,5$ this gives the results in the Table.

How the chance nobody wins depends on number of tickets sold
Number of tickets sold % Chance nobody wins
$N$ 37%
$2N$ 13%
$3N$ 5%
$4N$ 2%
$5N$ 1%