Probability and Statistics
"The probability of showers Tuesday is 80%."
"The odds of the Detroit Tigers winning two consecutive baseball games is 20 to 1”.
“The likelihood of winning the lottery is 1 in 250,000."
"The frequency of death in an auto accident is 0.000176."
We deal with probability most every day in one form or another. The law does as
well: "probable cause," "probative," "probability of an accidental match," "weight of
evidence," and "beyond a reasonable doubt" are all probability terms used in our legal
system.
Can evidence be quantified?
Can evidence be valued numerically, like odds at a horse race? Probability (P) is the
likelihood that a certain event will occur. If P = 0, the event will not occur; that is, it
will occur 0% of the time. If P = 1, the event will definitely occur; that is, it will occur
100% of the time. Probability is calculated as a ratio of the number of actual
occurrences to the total of observations. So, for example, assume your class has 24
students. The probability of someone wearing something red in your class may be 6
out of 24, or 1 out of 4. So,
Probabilities are often reported in decimal form by multiplying by 100. So, the
probability of someone in your class wearing red is (.25)(100) = 25%.
If there are 850 students in your school, how many of those students should be
wearing something red? Statistically one of every 4 should be wearing something
red, so:
(Probability in decimal form) x (Population) = (Number of Occurrences)
.25
x
850 = 213
So, statistically, there should be 213 students in the
school wearing something red.
Let’s try another problem: A different class in your
school has 19 students (your school still has 850
students). Only two students in that class are wearing
something yellow. Calculate the probability of a student
in that class wearing yellow, and determine the number of
students in your school wearing something yellow.*
Wearing something red or wearing something yellow are
Probability
is the
likelihood
that a
certain
event will
occur.
examples of independent events, which are events that are
independent of other events.
Now, let’s assume both red and yellow fabric were found near some graffiti in the
school bathroom, and you are asked to determine the number of students in your school
wearing both red and yellow. To do this, multiply the probabilities of each independent
event:
(P of wearing red) x (P of wearing yellow) = (P of wearing red AND yellow)
Dividing 2 by 76 gives the probability of finding a student in your class wearing red
and yellow as P = .026, or 2.6%. Please note, this method works ONLY if the events
are independent! If, for instance, people who wear red are likely to also wear yellow
because the two colors are complimentary, then you would need to introduce more
complex statistical procedures. In this course, though, we will deal only with
independent events.
Practice: How many students in your school (850 students) would be wearing BOTH
red and yellow?**
These probabilities are gained statistically. You may find that there are more or fewer
students wearing a combination of red and yellow. The Rule of Large Numbers
says that the larger the population, the more likely that the actual numbers will
approach those of the computed probability; that is, the larger the population you are
considering the more likely your calculated number of occurrences will be correct.
Correctly calculating probabilities is critical to making a strong case in court; many
cases have been thrown out of court or lost because the computed probability of a
random match of evidence has been overestimated.
Answers:
* P = 2/19, or .105, or 10.5%; 89 students
** 22 students
Probability and Statistics
Complete the following in your bound
journal.
1. Usually, evidence is used to link or associate a suspect to a crime. More
often than not, the evidence is class evidence. For example, a blue fiber is
found at a crime scene. Look at your classmates; how many could have
transferred a blue fiber from the clothes they are wearing? How many
suspects, then, are in your class?
2. Suppose the entire student body (650 students) had access to the crime site.
How many suspects would there be based on the statistics from your class?
(Clearly show all relevant calculations!) Is the blue fiber evidence of value?
That is, does it do a good job of reducing the number of suspects down to a
small number?
3. Suppose that along with the blue fiber, an orange fiber was also found.
Does the combination of a blue fiber and an orange fiber improve the
evidentiary value? Explain why. (Clearly show all relevant calculations!)
4. Does the number of characteristics of a material and/or the number of
different, relevant objects found at a crime scene improve the probability of
matching the evidence to a single suspect? Why or why not?
5. Camden has the following demographics:






Female residents
Male residents
Unmarried residents
Asian residents
American Indian residents
Caucasian residents
2206
1787
1712
20
2
3937
a) A suspect is described as a male, Asian resident of Camden. How many
people fit that profile? Would that characterization be of value?
b) A suspect is described as a female, married, and Caucasian. How many
people fit that profile? Would that characterization be of value?