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]]
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:- | -: | -: | -: | -: | -: |
**Duds**|$0$ | $1$ | $2$ | $3$ |$4$
**Winnings** | $\$1000$|$\$700$|$\$500$|$\$100$|$\$0$