Simple Probability FormulaReference > Mathematics > Probability
In the previous section, we were able to recognize whether an event was impossible, guaranteed, likely, unlikely, or equally likely to happen or not happen. It would be nice, though, if we had a mathematical formula which would help us determine just how likely or unlikely something is to happen.
Here's the formula:Probability =
Desired outcomes: If we're being asked for the probability of something happening, "desired outcomes" is the number of ways that the "something" could happen.
Possible outcomes: Possible outcomes is the number of ways an event could happen, regardless of whether or not we get the "desired" outcome. We also refer to the "possible outcomes" as the "sample space."
It's pretty simple to use, so let's dive right into an example.
I roll a six-sided die. What is the probability that I will roll a two?
How many ways can the six-sided die land? It can land in 6 different ways (1, 2, 3, 4, 5, or 6). Of these six, how many are "desired" outcomes (an outcome I want). There is only one desired outcome - a two. Thus, since there are 6 possible outcomes, and only 1 desired outcome:
I roll a six-sided die. What is the probability that I will roll a prime number?
There are still 6 possible outcomes, but now the number of desired outcomes has changed. Now we are hoping for either 2, 3, or 5 to appear, since those are all primes. How many desired outcomes? Three!
Note that this means we are just as likely to get a prime as to not get a prime.
I take a card from a 52 card deck. What is the probability the card will be an ace?
There are 52 possible outcomes. Of those, there are 4 desired outcomes (ace of spades, ace of hearts, ace of diamonds, and ace of clubs).
I take a card from a 52 card deck. What is the probability that it is a 14?
There are 52 possible outcomes. There are no desired outcomes, since there are no fourteens in the deck.