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What is a Dependent Event in Statistics?

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What is a Dependent Event in Statistics?

In probability, a dependent event is an event that relies on another event to happen first. Dependent events in probability are no different from dependent events in real life: If you want to attend a concert, it might depend on whether you get overtime at work; if you want to visit family out of the country next month, it depends on whether or not you can get a passport in time.

What is a Dependent Event in Statistics? Dependent event definition

When two events are dependent, the occurrence of one event influences the probability of another event.

Simple examples of dependent events:

  • Parking illegally and getting a parking ticket. Parking illegally increases your odds of getting a ticket.
  • Buying ten lottery tickets and winning the lottery. The more tickets you buy, the greater your odds of winning.
  • Driving a car and getting in a traffic accident.

Independent event definition

Whith two independent events, one event influences the probability of another event.

Simple examples of independent events:

  • Buying a lottery ticket and finding a penny on the floor (your odds of finding a penny does not depend on you buying a lottery ticket).
  • Taking a cab home and finding your favorite movie on cable.
  • Getting a parking ticket and playing craps at the casino.

What is a Dependent Event in Statistics? Card example

What is a Dependent Event in Statistics?

The probability of picking this particular jack is 1/3.


Cards are often used in probability as a tool to explain how one seemingly independent event can influence another. For example, if you choose a card from a deck of 52 cards, your probability of getting a Jack is 4 out of 52. Mathematically, you can write it like this:
P(Jack) = number of Jacks in a deck of cards / total number of cards in a deck = 4/52 = 1/13 ≈ 7.69%.

If you replace the jack and choose again (assuming the cards are shuffled), the events are independent. Your probability remains the same (1/13). Choosing a card over and over again would be an independent event, because each time you choose a card (a “trial” in probability) it’s a separate, non-connected event.

But what if the card was kept out of the pack the next time you choose? Let’s say you pulled the three of hearts, but you’re still searching for that jack. The second time you pull out a card, the deck is now 51 cards, so:
P(Jack) = number of Jacks in a deck of cards / total number of cards in a deck = 4/51 = 1/13 ≈ 7.84%
The probability has increased from 7.69% (with replacement of the jack) to 7.84% (the jack isn’t replaced), so choosing cards in this manner is an example of a dependent event.

More on this topic:
How to tell if an event is dependent or independent.

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What is a Dependent Event in Statistics? was last modified: October 24th, 2017 by Stephanie Glen