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 $6$ pitches, each at $60\text{ mph}$. Tyrell estimates that he will hit each individual pitch $90\%$ of the time. If Tyrell can hit all $6$ pitches, he will win a total of $\$50$; otherwise he will lose $\$50$. **The Fast Ball Challenge:** There will be $3$ pitches, each at $90\text{ mph}$. Tyrell estimates that he will hit each individual pitch $70\%$ of the time. If Tyrell can hit all $3$ pitches, he will win a total of $\$40$; otherwise he will lose $\$10$. **What are Tyrell's expected winnings from playing The Slow Ball Challenge? Round your answer to the nearest dollar. $\$$[[☃ math-keypad 1]]** **What are Tyrell's expected winnings from playing The Fast Ball Challenge? Round your answer to the nearest dollar. $\$$[[☃ math-keypad 2]]** **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 $5$ times. If Tyrell wants to maximize his expected winnings, what should he do?** [[☃ radio 1]]