Do you have some equation for how that works?

To calculate the probability of a specific series of events, all you have to do is multiply the probability of each individual step in the series.

Every time you take a turn while sneaking, you have a 5% chance of being noticed and a 95% chance of not being noticed, right? So the probability of not being noticed after two turns is just the probability of not being noticed after one turn (95%) multiplied by itself (so 95% times 95%).

95% is just another way of writing 0.95, and 0.95 * 0.95 = 0.9025, so the odds of not being noticed after two steps is 90.25%.

If you want to find out the odds of not being noticed after ten turns, it's 0.95 to the tenth power, or 0.95 * 0.95 * 0.95 * 0.95 * 0.95 * 0.95 * 0.95 * 0.95 * 0.95 * 0.95, which is about 0.6, so that's a 60% chance of not being noticed after ten turns.

The same formula works for anything. When flipping a coin, you have a 50% chance of getting heads. The probability of getting heads twice in a row is 0.5 to the second power (0.5 * 0.5) which equals 25%.

You can combine totally unrelated things together and it still works. If I flipped a coin and took two steps while sneaking, the probability of both getting heads and not being noticed is 0.5 * 0.95 * 0.95 = 0.45125, or 45.125%

Does this make sense?