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Statistics for Lawyers
Problem Set # 1– Due /04
Name_________________________________(Please Print)
1. In a civil case, the standard of proof is “more likely than not,” and in a criminal case it is
“beyond a reasonable doubt.” Do these standards import classical or Bayesian
probability?
Ans.__________________________________________________________________________
2. Rule 401 of the Federal Rules of Evidence defines “relevant evidence” in part as
“evidence having any tendency to make the existence of any fact that is of consequence to
the determination of the action more probable...than it would be without the evidence.”
(A)Taking H as the fact of consequence and E as the evidence, write the expression for
the likelihood ratio associated with the evidence. (B) What values of the likelihood ratio
would make the evidence relevant?
Ans.(A)_________________________________(B)___________________________________
3. One-third of a group of people receive a defective vaccine; two-thirds of the group the
modestly helpful vaccine. Studies show that with the defective vaccine 3/4 of the group
will get the disease and with the good vaccine 1/4 of the group will get the disease. A
person from the group gets the disease. Use Bayes’s theorem to compute the probability
that the person received the defective vaccine.
Ans.__________________________________________________________________________

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4. In attempting to tie a suspect to a shooting crime, the FBI determines whether two bullets
(a crime-scene bullet and a bullet or bullets owned by a suspect) were manufactured from
the same melt of lead. The Bureau does this by measuring the concentration of seven
trace elements in the bullet leads. If all seven match (within measurement error) the
bullets are declared probably to have come from the same melt. If the bullets come from
the same melt, 90% of the time the test will detect it. If they come from different melts,
there is 1 chance in 2400 that they will mistakenly be declared to have come from the
same melt. The reason for this is that some melts have the identical concentrations of
trace elements (within measurement error).
(A) Can the expert properly testify that the bullets came from the same melt with
probability 2399/2400?
(B) What can the expert properly say about the probability that two bullets that
have matching concentrations of trace elements came from the same melt?
Ans. (A)_________________________________________________________________
(B)_________________________________________________________________
End of Problem Set # 1