According to Error Management Theory, when making decisions under conditions of uncertainty, two kinds of errors need to be taken into account - "false positives", i.e. deciding that a risk or benefit exists when it does not, and "false negatives", i.e. failing to notice a risk or benefit that exists. False positives are also commonly called "Type 1 errors", and false negatives are called "Type 2 errors".
Where the cost or impact of a type 1 error is much greater than the cost of a type 2 error (e.g. the water is safe to drink), it can be worthwhile to bias the decision making system towards making fewer type 1 errors, i.e. making it less likely to conclude that a particular situation exists. This by definition would also increase the number of type 2 errors. Conversely, where a false positive is much less costly than a false negative (blood tests, smoke detectors), it makes sense to bias the system towards maximising the probability that a particular (very costly) situation will be recognised, even if this often leads to the (relatively un-costly) event of noticing something that is not actually there. This situation is exhibited in modern airport screening -- maximizing the probably of preventing a high cost terrorist event results in frequent, low-cost screening hassles for harmless travelers who represent a minimal threat.
Martie G. Haselton and David M. Buss (2003) state that cognitive bias can be expected to have developed in humans for cognitive tasks where:
The costly information hypothesis is used to explore how adaptive biases relate to cultural evolution within the field of dual inheritance theory. The focus is on the evolutionary trade-offs in cost between individual learning, (e.g., operant conditioning) and social learning. If more accurate information that could be acquired through individual learning is too costly, evolution may favor learning mechinisms that, in turn, are biased towards less costly, (though potentially less accurate), information via social learning.