Probability and Statistics > Basic Statistics> What is a Dependent Event in Statistics?

## 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

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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