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Making decisions with expected values

Tyrell is at the batting cage, where the owners are currently offering batting cage customers their choice of The Slow Ball Challenge or The Fast Ball Challenge.
The Slow Ball Challenge: There will be 66 pitches, each at 60 mph60\text{ mph}. Tyrell estimates that he will hit each individual pitch 90%90\% of the time. If Tyrell can hit all 66 pitches, he will win a total of $50\$50; otherwise he will lose $50\$50.
The Fast Ball Challenge: There will be 33 pitches, each at 90 mph90\text{ mph}. Tyrell estimates that he will hit each individual pitch 70%70\% of the time. If Tyrell can hit all 33 pitches, he will win a total of $40\$40; otherwise he will lose $10\$10.
What are Tyrell's expected winnings from playing The Slow Ball Challenge? Round your answer to the nearest dollar. $\$
What are Tyrell's expected winnings from playing The Fast Ball Challenge? Round your answer to the nearest dollar. $\$
The batting cage is allowing customers to participate in their choice of either The Slow Ball Challenge or The Fast Ball Challenge a total of 55 times. If Tyrell wants to maximize his expected winnings, what should he do?
Choose 1 answer:
Choose 1 answer: