Life is full of decisions.

In both pop culture and conventional wisdom, there is a common and understandable emphasis on individuals’ big decisions — the so-called points at a crossroad. It’s also true, though, that a series of smaller, everyday decisions can be just as important — if not more important — in determining one’s outcomes.

Essentially, it’s not because the smaller daily decisions have more inherent risk, but because they can be more frequent; the chance of an undesired outcome eventually happening for a repeated event actually increases due to an accumulation of risk.

Let’s say that you consider the number 4 unlucky. If you roll a six-sided die six times, what is the chance that you will roll at least one 4?

• A) (1/6) * (6) = 1 * 100 = 100%
• B) (1/6)⁶ = 0.0000214 * 100 = about 0.00214%
• C) (1/6) = 0.1667 * 100 = about 16.67%
• D) 1-(5/6)⁶ = 0.6651 = about 66.51%

The answer is D),the percentage probably intuitively making sense. The more chances you get, it feels like the chances are higher. It’s more the equation that goes into the answer that makes it interesting.

The wrong answers

First of all, in **A) **we intuitively can feel that it’s certainly possible — some would say unlucky — to never roll a 4.

**B) **is incorrect; rather, it’s calculating the chance that you roll a 4 six times in a row (you get six chances, and each time you have one-sixth of a chance). Needless to say, it’s pretty unlikely, and in the 0.00214% chance it does happen, perhaps you should consider that the universe may be trying to tell you something.

C) is also wrong, but perhaps your mind first went there. It’s understandable; each roll of the die carries a 1/6th chance, so maybe the overall chance is 1/6. The thing is that a 1/6th chance only applies with one roll of the die; with six, you’re getting multiple chances to get an undesired roll of a 4.

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