Question: Whenever Randy pitches to Chris, he throws either a fastball or a slider. When Randy pitches a fastball, Chris hits the ball with a probability

Whenever Randy pitches to Chris, he throws either a fastball or a slider. When Randy pitches a fastball, Chris hits the ball with a probability of .25 when he anticipates a fastball, and hits the ball with a probability of .1 when he anticipates a slider. When Randy pitches a slider, Chris hits the ball with a probability of .15 when he anticipates a fastball, and hits the ball with a probability of .3 when he anticipates a slider. Determine the optimal strategies for Randy and Chris, and the corresponding expected probability that Chris will hit the ball?

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