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In a horse race, there are two horses, namely, BridgeCrosser and PortJumper. Our old friends Nancy and Mark are trying to decide to bet on the winner or not. The race has been going on for the last six hours and consists of totally four steps. So far three of the steps are completed and PortJumper currently has 2 points leaving BridgeCrosser with 1 point. According to the rules, the owner of the losing horse has the right to decide on the next (final) step. If the owner decides on a 100 meter race, the winner gets 1 point, if the owner decides on a 500 meter race, the winner gets 2 points. The rules of the bet are explained below:
If the owner decides on a 500m. and if BridgeCrosser wins Nancy gets $5.
If the owner decides on a 500m. and if BridgeCrosser doesn’t win Nancy gives $2.
If the owner decides on a 100m. and if BridgeCrosser wins Nancy gets $1.
If the owner decides on a 100m. and if BridgeCrosser doesn’t win Nancy gives $2.
Assume that the owner is going to decide on a 100m. race with a probability of pr. The probability that BridgeCrosser wins the 100 m. race is ph and the probability that BridgeCrosser wins 500 m. race is pf. Assuming that, Nancy and Mark are trying to decide after the owner makes his/her decision. If Nancy is going to bet, what does she believe? (The probabilities need to be calculated)
(Please note that, in addition to the providing the solution, you need to determine the random events, decisions, random events that can occur, draw the Influence diagram, and draw the accompanying decision tree.)
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