An event is dependent if its probability
is affected by whether or not another event has occured.
A Real Example of a Dependent Event
It is easier to understand a dependent event with an example.
If a card is picked from a pack, 1
card is picked from a deck of 52
cards. The probability is 1⁄52
If the card that has been picked is not put back into the deck, there will be 1 less card in the deck.
If a 2nd
card is picked from the deck, 1
card is picked from a deck of 51
cards. The probability is 1⁄51
Picking cards without replacement are dependent events.
Picking coloured marbles from a bag, without replacing them, gives another example of dependent events.
The slider below shows how the probabilities of picking a certain colored marble changes depending on whether that color has been picked before.
An Event Is Dependent If the Probability Changes When It Is Repeated
Probability depends on the number of ways an outcome can occur and how many outcomes there are for an event.
For example, when tossing a coin, there is always 1
way a Heads
can come up and 2
These don't change no matter how many times a coin is tossed.
Now consider picking the Ace of Spades
from a pack of cards, without replacing it.
In the 1st
pick, there are 52
possible outcomes (one for each card).
In the 2nd
pick, one card has been removed...
...so the number of possible outcomes has changed...
...so the probability has changed...
...so the event is dependent.