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Probability using dice

When talking about the uncertainties expressed in any of the climate change projections, it is important to understand that any of the range of outcomes is possible. In-effect we have only got one roll of the dice. However, I need to focus in on a range ...place my bets. Looking at the results of rolling 2 dice: there is a 1-in-6 chance of rolling a 4-or-less; and a similar 1-in-6 chance of rolling a 10-or-more. Discounting those as unlikely futures, I am going to look at the 67% probability band, which is equivalent to rolling anything between 5 and 9.

The first table shows all of the results that you can get from rolling 2 dice. You can take these results and count the number of possible outcomes, for example there are 4 possible combinations of rolling dice that add up to 5 (i.e. 1&4, 2&3, 3&2 and 4&1). The following chart and table show this distribution.

A similar exercise is carried out with the results of climate model runs. In these cases though, there are usually thousands of results. The following graph shows probability curves of low, medium and high emission scenarios, from the UK Climate Projections. Any of those results is possible: for example, for the low emission scenario, temperatures could be anywhere between about 0ºC and about 6ºC ... in the same way that rolling 2 dice would give you a result of between 2 and 12. However, if we pick the same bands as I used above, there's about a 67% chance that the low emission scenario temperatures will be between about 1ºC and about 3.5ºC.