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Two terms that students often confuse in statistics are outcome and event.
Here’s the subtle difference between the two terms:
Outcome: The result of a random experiment.
- For example, there are six potential outcomes when rolling a die: 1, 2, 3, 4, 5, or 6.
Event: A set of outcomes that has a probability assigned to it.
- For example, one possible “event” could be rolling an even number. The probability that this event occurs is 1/2.
The following examples show more scenarios that illustrate the difference between outcomes and events.
Example 1: Deck of Cards
Suppose we randomly draw a card from a standard deck of 52 cards.
The four possible outcomes for the suit of the card include:
- Heart
- Spade
- Diamond
- Club
One of these four outcomes must occur.
However, there are many different events that we may be interested in assigning a probability to. For example:
Event 1: Draw a Heart
- The probability that this event occurs is 13/52 or 1/4.
Event 2: Draw a Heart or a Spade
- The probability that this event occurs is 26/52 or 1/2.
- The probability that this event occurs is 39/52 or 3/4.
There are many more events that we could come up with and assign a probability to, but these are just three simple ones.
Example 2: Pulling Marbles from a Bag
Suppose a bag has 3 red marbles, 5 green marbles, and 2 blue marbles.
If we close our eyes and randomly select one marble from the bag, the three possible outcomes for the color of the marble include:
- Red
- Green
- Blue
One of these four outcomes must occur.
However, there are many different events that we may be interested in assigning a probability to. For example:
Event 1: Draw a Blue Marble
- The probability that this event occurs is 2/10 or 1/5.
Event 2: Draw a Blue or Green Marble
- The probability that this event occurs is 7/10.
Event 3: Draw a Marble that is not Blue
- The probability that this event occurs is 8/10 or 4/5.
These are three events that we can easily calculate probabilities for.