If there is a 40% chance that you will get a red light at a certain traffic intersection, what is the probability of you passing through the intersection with green lights three times in a row?

To solve this probability puzzle, the first step is to flip the initial information around. If the chance of encountering a red light is 40%, then the probability of it being green must be the remaining 60% (or 0.6). This is because, for the sake of this problem, the only two outcomes are red or green, and their probabilities must add up to 100%. So, for any single trip through the intersection, you have a 6 in 10 chance of not having to stop.

The key to finding the probability of a sequence of events is to understand that each trip to the intersection is an independent event. The traffic light's color on Monday has no memory of what it was on Sunday. To calculate the odds of three independent events happening in a row, you multiply their individual probabilities together. In this case, you would multiply the probability of getting a green light (0.6) by itself three times: once for the first trip, once for the second, and once for the third.

This calculation (0.6 x 0.6 x 0.6) reveals that there's a 0.216, or 21.6%, chance of getting lucky with three consecutive green lights. This same principle of multiplying independent probabilities is fundamental in many fields, from forecasting weather patterns to determining risk in the insurance industry. It also demonstrates how quickly the odds of a "streak" decrease. While a single green light is a likely outcome, hitting three in a row is significantly less certain.