When the court hears the case it finds the probability of truth for each fact.
These findings are set out in the following table:
Fact
True
False
Total
Fact 1
60%
40%
100%
Fact 2
80%
20%
100%
Fact 3
75%
25%
100%
Fact 4
60%
40%
100%
Figure 9.3 Independent Facts
Having found the probability that each specific fact is true or (false), the court
now has to proceed to its main task in finding facts, to determine the
probability that all of the facts are true (because by doing this it can determine
if the plaintiff has sufficiently proved their case). Since the facts are
independent we use the product rule. To calculate this overall probability we
multiply together the probability for each specific fact, Facts 1-4 in the
illustration. This gives us the probability that all of the facts are true:
Probability
= P (Fact 1) x P (Fact 2) x P (Fact 3) x P (Fact 4)
= (0.60) x (0.80) x (0.75) x (0.60)
= 0.216
= 21.6%
Figure 9.4 Illustration of the Multiplication Rule
This shows us that the probability that each of the four facts in the plaintiff’s
case is absolutely true is 21.6%. Just to round off the illustration let us explain
how a court uses this information to work out who wins the case and who
loses. In a civil case, as we noted above, a plaintiff must prove their case on
the balance of probabilities, ie to a probability of 51%. Here the probability of
the plaintiff’s case is only 21.6%. This is less than the 51% which the plaintiff
requires, so the plaintiff fails to prove her case and loses.
Subsidiary Rules
In the illustration above, the probabilities for Facts 1-4 were respectively 60%,
80%, 75% and 60%. The probability that all four facts, Facts 1-4, were
absolutely true is 21.6%. We can use this result to illustrate two subsidiary
rules which are of general application but which also help us to understand
more about how probability is used in fact finding.
Rule 1: Result Lower Than Lowest Individual Score
In using the product rule we multiply a number of specific probabilities
together. These are essentially fractions. Because of this, by multiplying them
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