Imagine that the outcome of the first event is a four of hearts. After drawing the four of hearts, without replacement we draw a second card. Let B be the event that we draw a four again. Notice that, because we did not replace the card, we cannot draw a four of hearts for a second time.
We can see that the outcome of event A influences the outcome of event B. This means that the events are dependent events. Dependent events will also affect the probability of one another. The following list is comprised of other examples of dependent events.
Drawing a name from a hat and throwing it away before drawing a second name
Driving in a car and getting stuck in a traffic jam
Buying a lottery a ticket and winning the Mega Millions
Now, let's consider the new standard deck of cards. However, this time, we will draw cards with replacement. Let C denote the event that we draw a two.
After replacing the first card, we draw a second card. Let D be the event that we draw a two again. Since we replaced the first card, the outcome of the first event will not affect the outcome of the second event. Therefore, events C and D are independent events. Independent events do not affect the probability of one another. Let's take a look at some examples of independent events.
Rolling two dice
Flipping a quarter and then flipping a nickel
Eating spaghetti for dinner and being late to school
Finally, we can summarize the differences between dependent and independent events.
Differences
Dependent Events
Independent Events
The outcome of one event influences the outcome of the second event.
The outcome of one event does not influences the outcome of the second event.
The outcome of one event affects the probability of the second event.
The outcome of one event does not affect the probability of the second event.
