#### Inconsequential

##### New member

- Joined
- Apr 17, 2021

- Messages
- 3

Mr. A believes that the Democrat will be elected in a presidential election with probability 5/8. Mr.B 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 Mr.A will pay Mr.B $10 if the Republican wins, and Mr.B will pay him $10 if the Democrat wins.)

- What is Mr.A’s expected dollar gain?
- What is Mr.B’s?
- How would you be able to make money for sure by betting with Mr.A and Mr.B if they are both always ready to accept any bet that they believe has a nonnegative dollar expectation?

According to Mr.A, Democrat will win with probability 5/8, it means probability of a republican win is 3/8 in his case.

According to Mr.B, 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.