The concept of causation is a fundamental one in philosophy and science. Causation refers to the relationship between events, or the way events relate to each other as causes and effects.
How do we know that one event causes another event, rather than the other way around? Or how do we know that they are not related at all?
As philosopher David Hume (1711-1776) noted, we cannot prove that one event causes another unless we have observed every instance of one event and only that event occurring before the other.
This is because we cannot prove that there are no other events that may have preceded the ones we are investigating. We may think A caused B, but how can we be sure there was not some other cause C?
Causes can be difficult to identify, which is why many studies focus on associations rather than direct causes. An association is when one event occurs and there is some likelihood of another event occurring as well.
Dependent
Another way in which events can be linked is when one event affects the outcome of a second event. This is referred to as dependent events.
When one event affects the outcome of a second event, they are linked in some way. Dependent events are defined as events that are linked in such a way that the existence or occurrence of one event depends on the existence or occurrence of the other.
For example, voting for candidate A will result in policy P being implemented. Policy P is not going to be implemented regardless of whether or not someone votes for candidate A, but voting for candidate A will ensure that it does. This is a dependent event because whether or not someone votes for candidate A depends on whether or not policy P is implemented.
Dependent events can also be negative. For example, person A may have a bad knee, which causes them to walk with a limp. Walking with a limp results in person A getting wet feet, which causes them to get sick.
True independent events
When events are said to be independent, this means that the outcome of one event does not affect the outcome of the other event. When events are not independent, then the outcome of one event can affect the outcome of the other event.
For example, if you toss a coin, its result will be heads or tails. If you toss a coin twice, the result will be two heads or two tails.
If you roll a die, its result will be a specific number. If you roll a die twice, the second number will not be affected by the first number.
These events are independent of each other. However, in real life, almost all events that we encounter are not independent of each other.
In fact, very few events in our life are truly independent of each other.
False independent events
When two events are said to be false independent, that means that the outcome of one event does not affect the outcome of the other event. When this is true, you can calculate the probability of one event knowing the probability of the other event.
For example, if you roll a die once and it comes up six, then you can say that the die is fair (each side is a 1/6 chance of being picked) and that there is no influence on the outcome whether or not you shake the die before picking a side.
Shaking the die before picking a side has no influence on what side comes up, so rolling a six is independent of whether or not you shake the die before rolling it. This is true because if you were to shake the die before rolling it 100 times, then you would get roughly 100 sixes.
Independent does not mean impossible coincidence
Another common myth about dependent and independent events is that if one event happens, then the other event is impossible. This is not true!
For example, if a person buys a lottery ticket, then they will probably win the money. The fact that they bought a lottery ticket does not make them less likely to win, it makes them more likely to win!
This is because buying a lottery ticket is not affecting the outcome of whether or not they win. Whether they buy a ticket or not will not affect whether or not they win.
They are independent events because one does not affect the other. Even though buying a lottery ticket may make someone more likely to win, it does not make them any less likely to win either.
Dependent events with probability of occurrence of A affecting B
If the outcome of event A affects the outcome of event B, then A and B are dependent events.
For example, if you go to the gym every day, then you are more likely to lose weight than if you did not go to the gym every day.
The two events here are going to the gym and losing weight, so losing weight is an outcome of going to the gym. These two events are dependent on each other.
If you go to the gym every day, then you will most likely lose weight. This is because going to the gym increases your chances of exercising effectively, which in turn increases your chances of losing weight.
Summary of the independence and dependence concepts
In summary, independence refers to the circumstance that the outcome of one event does not depend on the occurrence or non-occurrence of another event. That is, if event A occurs, then the probability that event B occurs remains the same.
Dependence refers to the circumstance that the outcome of one event does depend on the occurrence or non-occurrence of another event. That is, if event A occurs, then the probability that event B occurs changes depending on whether or not event A occurred.
Two events are said to be independent if neither affects the probability of the other. Two events are said to be dependent if one affects the probability of the other.
Independence and dependence apply to all events, including binary (two-outcome) events. The concept of independence applies only to two events; for N (N-outcome) events, there are (N − 1) types of independence.
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