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Probability: Fallacies, Myths and Puzzles: Main Page

A footballer or a nurse?

 Suppose 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 description)  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 particular 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 no 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 concluded that when no specific evidence is given, prior probabilities are used properly; when worthless evidence is given, prior probabilities are ignored.

Norman Fenton

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