Two events are independent if the occurrence of one event does not affect the probability of the second event also occurring.
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Practice makes perfect
We want to give an example of two independent events. Events are independent if the occurrence of one event does not affect the probability of the second event also occurring. Let's imagine that there are two possible ways to go to the market and we flip a coin to choose our path.
After we arrive at the market, we need to choose which snack we want. Because we do not have any preference for our snack today, we decide to roll a six-sided die to choose 1 out of the 6 possible options.
Note that flipping the coin will not affect rolling the die. This means that the choice of the path we take will not influence the probability of choosing our snack. Therefore, the events are independent. Let's consider some other real-world examples of two independent events.
Rolling two dice one at a time
Winning the lottery and running out of orange juice
Taking a cab home and choosing a TV show to watch
In general, showing that events are independent events can be difficult, because we need to be sure that they do not influence each other at all. Although in real-world scenarios it is usually not the case, we may treat events as independent if their influence on each other is very unlikely.
