Adam is entering The Hammer County Firework Contest with $4$ high intensity fireworks. Each firework has a $50\%$ chance of being a dud and therefore not leaving the ground independent of the other fireworks. The table below shows how much Adam will win depending on how many of his fireworks are duds. **What is Adam's expected winnings from The Hammer County Firework Contest?** Round your answer to the nearest cent. $\$$ [[☃ input-number 1]] |||||| :- | -: | -: | -: | -: | -: | **Duds**|$0$ | $1$ | $2$ | $3$ |$4$ **Winnings** | $\$1000$|$\$700$|$\$500$|$\$100$|$\$0$