Now suppose that you suffer from confirmation bias. You are pretty sure that it is going to be sunny, so you misinterpret rain forecasts as sun forecasts 20% of the time but always correctly interpret sun forecasts. You are aware of your own confirmation bias. If your interpretation is that you have seen two sun forecasts, what is your updated belief about the probability of sun? Will you bring your umbrella?
Suppose you are deciding whether or not to bring an umbrella to school and the weather
can be either sunny or rainy. Initially, you think the probability that it will be sunny is
P(S)=0.6, and the probability that it will be rainy is P(R)=0.4. If you bring an umbrella and it
rains, your payoff is 6. If you bring an umbrella and it is sunny, your payoff is 9. If you don't
bring an umbrella and it rains, your payoff is O. If you don't bring an umbrella and it is sunny,
your payoff is 10.
Now suppose that you suffer from confirmation bias. You are pretty sure that it is going to
be sunny, so you misinterpret rain forecasts as sun forecasts 20% of the time but always
correctly interpret sun forecasts. You are aware of your own confirmation bias. If your
interpretation is that you have seen two sun forecasts, what is your updated belief about the
probability of sun? Will you bring your umbrella?
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