risk

Risk is the potential for harmful outcomes. In a statistical setting this is often assessed using the probability of each negative outcome and the potential loss. This is typically balanced against corresponding gains for positive outcomes.

The simplest case is to work out the expected gain and expected loss, and this is the correct process where the risky process is repeated many times and the scale of losses and gains means they 'average out' in the long run; as in the case with an insurance company. However, when the event that leads to the potential loss/gain is infrequent one might prefer to avoid high potential losses even if infrequent – this is precisely why one takes out insurance. Similarly one might be willing to accept frequent small costs in return for the prospect of an unlikely, but possible large gain – why people buy lottery tickets!