Dependent Events vs Independent Events

Learn about the differences between the two types of events

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What are Dependent Events vs Independent Events?

In mathematics, specifically statistics, events are often classified as dependent or independent. As a basic rule of thumb, the existence or absence of an event can provide clues about other events. Read on to find out more about dependent events vs independent events.

In general, an event is deemed dependent if it provides information about another event. An event is deemed independent if it offers no information about other events.

Dependent Events vs. Independent Events Diagram


  • In mathematics – namely statistics – as well as in real life, events are often categorized as either dependent or independent.
  • Dependent events influence the probability of other events – or their probability of occurring is affected by other events.
  • Independent events do not affect one another and do not increase or decrease the probability of another event happening.

What are Dependent Events?

For events to be considered dependent, one must have an influence over how probable another is. In other words, a dependent event can only occur if another event occurs first.

While this is a mathematic/statistical term, speaking specifically to the subject of probabilities, the same is true of dependent events as they occur in the real world.

For example, say you’d like to go on vacation at the end of next month, but that depends on having enough money to cover the trip. You may be counting on a bonus, a commission, or an advance on your paycheck. It also most likely depends on you being given the last week of the month off to make the trip.

The primary focus when analyzing dependent events is probability. The occurrence of one event exerts an effect on the probability of another event. Consider the following examples:

  1. Getting into a traffic accident is dependent upon driving or riding in a vehicle.
  2. If you park your vehicle illegally, you’re more likely to get a parking ticket.
  3. You must buy a lottery ticket to have a chance at winning; your odds of winning are increased if you buy more than one ticket.
  4. Committing a serious crime – such as breaking into someone’s home – increases your odds of getting caught and going to jail.

What are Independent Events?

An event is deemed independent when it isn’t connected to another event, or its probability of happening, or conversely, of not happening. This is true of events in terms of probability, as well as in real life, which, as mentioned above, is true of dependent events as well.

For example, the color of your hair has absolutely no effect on where you work. The two events of “having black hair” and “working in Allentown” are completely independent of one another.

Independent events don’t influence one another or have any effect on how probable another event is.

Other examples of pairs of independent events include:

  1. Taking an Uber ride and getting a free meal at your favorite restaurant
  2. Winning a card game and running out of bread
  3. Finding a dollar on the street and buying a lottery ticket; finding a dollar isn’t dictated by buying a lottery ticket, nor does buying the ticket increase your chances of finding a dollar
  4. Growing the perfect tomato and owning a cat

Additional Resources

Thank you for reading CFI’s guide to Dependent Events vs Independent Events. To keep learning and developing your knowledge of financial analysis, we highly recommend the additional CFI resources below:

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