caesar's last breath problem

Assume that caesar's last breath(air molecules) is still in the atmosphere.From the following assumptions calculate the required probability given below:

Assumptions: 1. The gas molecules from Caesar's last breath are now evenly dispersed in the atmosphere. 2. The atmosphere is 50 km thick, has an average temperature of 15 °C, and an average pressure of 0.20 atm. 3. The radius of the Earth is about 6400 km. 4. The volume of a single human breath is roughly 500 mL.

find the probability that we inhale an air molecule from caesar's last breath??

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Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$