3.2 Probability: Outside or Inside the Head 29 We can narrow down the degree of belief by considering other comparison gambles. Consider these two gambles: Gamble A. You get $100 if there is a traffic-stopping snowstorm in Indi- anapolis next New Year's Day. Gamble C. You get $100 if you draw a red marble from a sack of marbles with 1 red and 9 white marbles. Which gamble would you prefer? If you now prefer gamble A, that means you think there is more than a 10% chance of a traffic-stopping snowstorm in Indy on New Year's Day. Taken together, the two comparison gambles have told you that your subjective probability lies somewhere between 0.1 and 0.5. We could continue to consider preferences against other candidate gambles to calibrate your subjective belief more accurately. 3.2.2.2 Describing a Subjective Belief Mathematically When there are several possible outcomes in a sample space, it might be too much effort to try to calibrate your subjective belief about every possi- ble outcome. Instead, you can use a mathematical function to summarize your