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Probability equals the number
of ways a specified event can occur, divided by the total number of all
possible event occurrences. Probability can only range from values 0 to 1. A
probability of 0 means there are no possible outcomes for that event - a
probability of 1 means the event will occur in each and every trial
By Andrea Farkas
Probability
measures the likelihood of an event occurring.
Expressed
mathematically, probability equals the number of ways a specified event can
occur, divided by the total number of all possible event occurrences.
For
example, if you have a bag containing three marbles -- one blue marble and two
green marbles -- the probability of grabbing a blue marble sight unseen is 1/3.
There
is one possible outcome where the blue marble is selected, but three total
possible trial outcomes -- blue, green, and green.
Using
the same math the probability of grabbing a green marble is 2/3.
Law of Large Numbers
You
can discover the unknown probability of an event through experimentation.
Using
the previous example, say you do not know the probability of drawing a certain
colored marble, but you know there are three marbles in the bag.
At
this point you might claim the bag contains only green marbles, but based on
two trials, your prediction is not reliable.
It
is possible the bag contains only green marbles or it could be the other two
are red and you selected the only green marble sequentially.
If
you perform the same trial 100 times you will probably discover you select a
green marble around 66% percent of the time.
This
frequency mirrors the correct probability more accurately than your first
experiment.
This
is the law of large numbers: the greater the number of trials, the more
accurately the frequency of an event's outcome will mirror its actual
probability.
Law of Subtraction
Probability
can only range from values 0 to 1.
A
probability of 0 means there are no possible outcomes for that event.
In
our previous example, the probability of drawing a red marble is zero.
A
probability of 1 means the event will occur in each and every trial.
The
probability of drawing either a green marble or a blue marble is 1.
There
are no other possible outcomes.
In
the bag containing one blue marble and two green ones, the probability of
drawing a green marble is 2/3.
This
is an acceptable number because 2/3 is greater than 0, but less than 1-- within
the range of acceptable probability values.
Knowing
this, you can apply the law of subtraction, which states if you know the
probability of an event, you can accurately state the probability of that event
not occurring.
Knowing
the probability of drawing a green marble is 2/3, you can subtract that value
from 1 and correctly determine the probability of not drawing a green marble:
1/3.
Law of Multiplication
If
you want to find the probability of two events occurring in sequential trials,
use the law of multiplication.
For
example, instead of the previous three-marbled bag, say there is a five-marbled
bag.
There
is one blue marble, two green marbles, and two yellow marbles.
If
you want to find the probability of drawing a blue marble and a green marble,
in either order (and without returning the first marble to the bag), find the
probability of drawing a blue marble and the probability of drawing a green
marble.
The
probability of drawing a blue marble from the bag of five marbles is 1/5.
The
probability of drawing a green marble from the remaining set is 2/4, or 1/2.
Correctly
applying the law of multiplication involves multiplying the two probabilities,
1/5 and 1/2, for a probability of 1/10.
This
expresses the likelihood of the two events occurring together.
Law of Addition
Applying
what you know about the law of multiplication, you can determine the
probability of only one of two events occurring.
The
law of addition states the probability of one out of two events occurring is
equal to the sum of the probabilities of each event occurring individually,
minus the probability of both events occurring.
In
the five-marbled bag, say you want to know the probability of drawing either a
blue marble or a green marble.
Add
the probability of drawing a blue marble (1/5) to the probability of drawing a
green marble (2/5). The sum is 3/5.
In
the previous example expressing the law of multiplication, we found the
probability of drawing both a blue and green marble is 1/10.
Subtract
this from the sum of 3/5 (or 6/10 for easier subtraction) for a final
probability of 1/2.
Andrea
Farkas
has been writing since 2005. Her legal article appears in the "Texas Tech
Estate Planning" and "Community Property Law Journal." Farkas
graduated from Texas A&M University and earned her law degree from Texas
Tech University School of Law.
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