Between 5:00 PM and 6:00 PM, cars arrive at McDonald's drive-thru at the rate of 20 cars per hour. The following formula from probability can be used to determine the probability that $x$ cars will arrive between 5:00 PM and 6:00 PM. Complete parts (a) and (b).
\[
P(x)=\frac{20^{x} e^{-20}}{x !}, \text { where } x !=x \cdot(x-1) \cdot(x-2) \cdot \cdots \cdot 3 \cdot 2 \cdot 1
\]
(a) Determine the probability that $x=10$ cars will arrive between 5:00 PM and 6:00 PM.
$P(10)=\square($ Round to two decimal places as needed.)

Step 1 ：The problem is asking for the probability that exactly 10 cars will arrive at a McDonald's drive-thru between 5:00 PM and 6:00 PM, given that cars arrive at a rate of 20 cars per hour.

Step 2 ：We can use the given formula to calculate this probability: \(P(x)=\frac{20^{x} e^{-20}}{x !}\), where \(x !\) is the factorial of \(x\), and \(x\) is the number of cars.

Step 3 ：Substitute \(x=10\) into the formula: \(P(10)=\frac{20^{10} e^{-20}}{10 !}\).

Step 4 ：Calculate the result, which is approximately 0.005816306518345136.

Step 5 ：However, the problem asks for the answer to be rounded to two decimal places. So, we round the result to 0.01.

Step 6 ：Final Answer: The probability that exactly 10 cars will arrive between 5:00 PM and 6:00 PM is \(\boxed{0.01}\).