Final answer:
Without specific game details, we cannot accurately determine the probabilities or solution to the game between the shooter and keeper. Once details are provided, we could use Nash Equilibrium to calculate optimal strategies.
Step-by-step explanation:
The scenario presented is related to probability and requires finding solutions for a game scenario for two players, a shooter, and a keeper. Unfortunately, the specific information about the strategies, payoffs, or probabilities for the shooter and keeper in the game is missing. Without this information, it's not possible to answer the question correctly.
To provide a meaningful answer, we would typically use the concept of Nash Equilibrium in game theory, where each player's strategy is optimal, given the strategies of other players, resulting in no incentive for players to change their strategies. The shooter's and keeper's probabilities of choosing left, center, or right are interdependent on each other's strategies. Additionally, the shooter's expected probability of scoring would require knowledge of the strategies' effectiveness against one another.
As the specific game details are missing from the question, it's advised to obtain the game matrix or payoffs for the various strategies to calculate the solution accurately. Only then can we apply the appropriate methods to find the Nash Equilibrium and determine the probabilities for each player's strategy.