The Lesson
An event is independent if its outcome does not affect the
probability of other events occuring.
Real Examples of Independent Events
It is easier to understand independent events with examples.
Tossing a Coin
If a coin is tossed, the probability of it landing
Heads is
1⁄2.
If a coin is tossed a 2
nd time, the probability of it landing
Heads is still
1⁄2.
Each toss does not affect the probability of another toss. Coin tosses are independent events.
Rolling a Die
If a die is rolled, the probability of getting a
2 is
1⁄6.
If a die is rolled a 2
nd time, the probability of getting a
2 is still
1⁄6.
Each die roll does not affect the probability of another roll. Die rolls are independent events.
An Event Is Not Independent 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 outcomes (
Heads and
Tails).
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 1
st pick, there are
52 possible outcomes (one for each card).
In the 2
nd pick, one card has been removed...
...so the number of possible outcomes has changed...
...so the probability has changed...
...so the event is not independent.
)