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260 Biases in probability assessment
back-up machine both fail today’ or ‘you get promoted and win the lottery
and write a best selling novel all within the next 12 months’. Each of the
individual events which might co-occur is called an elementary event
(for example, ‘getting promoted’ is an elementary event). Research 10
suggests that people tend to overestimate the probability of conjunctive
events occurring because they anchor on the probability of one of the
elementary events and make insufficient adjustment from this. Consider
the following example.
For a communication system to work, each of seven independent relay
centers must be operational. Each center has a 0.9 probability of being
operational at any given moment. You are about to send a message
through the system. Estimate the probability that your message will
reach its destination.
It is likely that you will anchor on the 0.9 probability of one of
the centers being operational. If this is the case, you will overestimate
the true probability which (from the multiplication rule – see Chapter
4) is:
0.9 × 0.9 × 0.9 × 0.9 × 0.9 × 0.9 × 0.9 i.e. only 0.48.
As Tversky and Kahneman point out, the estimation of conjunctive
events is particularly important in planning. Projects such as the development
of a new product or the completion of a construction project on
time involve a series of elementary events, all of which must succeed
for the undertaking as a whole to be successful. While the individual
probability of each of the elementary events succeeding may be high,
the overall probability of success may be low. The tendency of people to
overestimate probabilities for conjunctive events may therefore lead to
unjustified optimism that the project will succeed.
Test your judgment: answer to question 12
Q12. Did you anchor on the 99.5% probability? The correct answer is
that the proposed safety system would only have a 47% probability
of being operational on any given day.
3. Underestimating probabilities for disjunctive events
Disjunctive events can be expressed in the form ‘either X or Y occurs’.
Examples would be ‘either the ignition system or the cooling system in