# Probability Problem

#### Iconoclast

##### New Member
Hello! I am stuck in a problem. The question is as follows.
Jay believes that the Democrat will be elected in a presidential election with probability 5/8. Mike believes the Republican will be elected with probability 3/4. Neither gives third party candidates any chance at all. They agree to bet $10 on the outcome at even odds. (Thus Jay will pay Mike$10 if the Republican wins, and he will pay him \$10 if the Democrat wins.)
What is Jay’s and Mike's expected dollar gain?
How would you be able to make money for sure by betting with Jay and Mike if they are both always ready to accept any bet that they believe has a nonnegative dollar expectation?

My attempt so far:
According to Jay, Democrat will win with probability 5/8, it means probability of a republican win is 3/8 in his case.
According to Mike, Republican will win with probability 3/4, it means probability of a democrat win is 1/4 in his case.
will it make sense if probabilities of democrat (and republican) win in both cases are added and find a solution.

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#### katxt

##### Active Member
I think you need to know the real probability that a Democrat will win.