Suppose you want to spend the weekend camping with your friends. Some of your friends

Suppose you want to spend the weekend camping with your friends. Some of your friends are
worried that it might rain during the weekend. Denote the state when it rains by ? = R and the
state when it does not rain by ? = NR. Given the weather during the last weeks, your prior is
that it will rain with probability P r(? = R) = 0.3. Your payoffs under different scenarios are given
by:
Go camping when it does not rain = 1
Go camping when it rains = -1
Not camping = 0
You want to maximize your expected payoff (i.e., the weighted average of payoffs, where weights
are given by the posterior probability of each event).
To get more information, you decide to watch the weather forecast on TV. They use a machine
learning algorithm that delivers a signal s indicating whether it will rain or not (s = r or s = nr).
The algorithm predicts the state of the world correctly only with probability a (where a > 0.5).
That is,

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