Probability
Probability is a measure of the likelihood that an event will happen.
When dealing with probability, the outcomes of a process are the
possible results. For example, when a die is rolled, the possible
outcomes are 1, 2, 3, 4, 5, and 6. In mathematical
language, an event is a set of outcomes, which describe what
outcomes correspond to the "event" happening. For instance, "rolling an
even number" is an event that corresponds to the set of outcomes
{2, 4, 6}.
The probability of an event, like rolling an even number, is the
number of outcomes that constitute the event divided by the total
number of possible outcomes. We call the outcomes in an event its
"favorable outcomes".
Probability = 

If a die is rolled once, determine the probability of rolling a
4: Rolling a
4 is an event with
1 favorable outcome (a
roll of
4) and the total number of possible outcomes is
6 (a roll
of
1,
2,
3,
4,
5, or
6). Thus, the probability of rolling
a
4 is
.
If a die is rolled once, determine the probability of rolling
at least a 4: Rolling at least
4 is an event with
3
favorable outcomes (a roll of
4,
5, or
6) and the total number
of possible outcomes is again
6. Thus, the probability of rolling at
least a
4 is
= .
Here are two more examples:
If a coin is flipped twice, determine the probability that it will land heads both
times:
Favorable outcomes: 1  HH
Possible outcomes: 4  HH, HT, TH, TT
Thus, the probability that the coin will land heads both times is .
If Dan grabs one sock from a drawer containing 3 white socks, 4 blue socks, and 5
yellow socks, what is the probability that he will grab a white sock?
Favorable outcomes: 3 (3 white socks)
Possible outcomes: 12 (3 white socks + 4 blue socks + 5 yellow socks)
Thus, the probability that Dan will grab a white sock is = .
Though probabilities are calculated as fractions, they can be
converted to decimals or percentsthe Fractions SparkNote
in PreAlgebra explains how to convert fractions to decimals
and the SparkNote on Percents describes how to
convert them to percents.
Boundaries on Probability
If all outcomes are favorable for a certain event, its probability is 1. For
example, the probability of rolling a 6 or lower on one die is = 1.
If none of the possible outcomes are favorable for a certain
event (a favorable outcome is impossible), the probability is 0.
For example, the probability of rolling a 7 on one die is
= 0.