Final answer:
The decision-making bias explaining why someone would ski in the rain after purchasing a two-day ski pass is called escalation of commitment, which involves continuing a course of action after an initial investment.
Step-by-step explanation:
The decision-making bias most likely to explain why you will ski in the rain, despite poor weather conditions, after having purchased a two-day ski pass is escalation of commitment. This bias describes a pattern where people are inclined to continue an endeavor once an initial investment of money, effort, or time has been made. This can be even in the face of new negative information or outcomes, such as bad weather, because of the desire to not waste the initial investment (in this case, the two-day pass).