or a nurse?
you are given the following description of a person:
'He is an
extremely athletic looking young man who drives a fast car and has an
attractive blond girlfriend.'
Now answer the following question:
Is the person most likely to be
a premiership professional footballer or a nurse?
If you answered professional
footballer then you were sucked into the fallacy of ignoring the
base-rate frequencies of the different professions simply because the
description of the person better matched the stereotypical image. In
fact there are less than 450 premiership professional footballers in
the UK (of whom at most 30 fit the above
compared with many thousands of male nurses in the UK alone, let alone
the rest of the world. So, in the absence of any other information it
is far more likely that the person is a nurse.
Anyway, you shouldn't
worry too much
if you went with the footballer. The experimentalists Kahneman and
Tversky (in 1973) showed that most people 'get it wrong'. In
their experiment subjects were shown brief personality descriptions of
several individuals, allegedly sampled at random from a group of 100
professionals - all engineers or lawyers. The subjects were asked to
assess, for each description, the probability that it belonged to an
engineer rather than a lawyer. There were two experimental conditions:
1. Subjects were told
the group consisted of 70 engineers and 30 lawyers
2. Subjects were told
the group consisted of 30 engineers and 70 lawyers
The probability that a
description belongs to an engineer rather than a lawyer should be
higher in 1 than in 2. However, in violation of Bayes rule, the
subjects produced essentially the same probability judgements. Subjects
were apparently evaluating the likelihood of a description being an
engineer rather than a lawyer by the degree to which it was
representative of the two stereotypes; they were paying little or no
regard to the probabilities of the categories.
When subjects were given
personality sketch, but were simply asked for the probability that an
unknown individual was an engineer the subjects correctly gave the
responses 0.7 and 0.3 in 1 and 2 respectively. However, when presented
with a totally uninformative description the subjects gave the
probability to be 0.5 in both experiments 1 and 2.
Kahneman and Tversky
when no specific evidence is given, prior probabilities are used
properly; when worthless evidence is given, prior probabilities are