A More Complex Example

At first blush, forensic thinking may appear to strip us of all investigative power and abandon us in murky waters where every conclusion is predicated on weasel-worded assumptions. This is absolutely not true. To illustrate, let's return to our dice example again. Let's assume we roll six sixes in a row on what appears to be a normal six-sided die. This makes us suspect a trick die that will only roll a six. The chance of rolling six sixes on a trick die that always lands on six is 1, because that is the only result we'll get. The chance of rolling a six six times on normal die is:

(1/6)x(1/6)x(1/6)x(1/6)x(1/6)x(1/6), or approximately 0.0000214.

Therefore, our odds of rolling six sixes when we compare the assumption of a trick die versus a normal die becomes:

1 divided by 0.0000214 or approximately 46,700 to one.

Which is a very strong argument in favor of a trick die, as the six sixes in a row are 46,700 times more likely with that die.

The advantage to this type of thinking is that it separates our assumptions from our analysis and draws them out into the open. Even if your assumptions are wrong, you can still remain confident in your analysis. However, a change in your assumptions will often require a different conclusion.