One recent estimate concludes that nearly 800 meteorites with mass greater than 100 grams (massive enough to cause personal injury strike the surface of Earth each day. Assuming you present a target of 0.25 square meter \(\left(\mathrm{m}^{2}\right)\) to a falling meteorite, what is the probability that you will be struck by a meteorite during your 100-year lifetime? (Note that the surface area of Earth is approximately \(5 \times 10^{14} \mathrm{m}^{2}\).)

Probability calculations help us determine the likelihood of events happening. In this exercise, we calculated the probability of being hit by a meteorite using several steps. We started with the total number of meteorites that fall on Earth each day and divided it by the Earth's surface area to find the daily probability of a meteorite striking any specific square meter.
To refine this probability for a 0.25 square meter area, we multiplied by the target area. Then, by considering multiple days, we scaled this up from daily to yearly probability, and finally to a lifetime probability. The result gives us a clear understanding of the chances over different time frames.
By converting the final value into a percentage, we can more intuitively understand the extremely low likelihood of such an event.

Understanding surface area is crucial in our problem. Earth's surface area is approximately \[ 5 \times 10^{14} \text{ m}^2 \].
Surface area is basically the measure of how much exposed area an object has. To put it into perspective, it’s like calculating the amount of wrapping paper needed to cover Earth entirely. For meteorite impacts, the larger the surface area, the more spread out the impacts will be.
When calculating probabilities, knowing the exact area being considered (both Earth's overall surface and your specific target area of 0.25 square meters) directly affects result. Larger areas present larger targets and hence higher probabilities of being struck.

Meteorite impacts are rare but fascinating phenomena. Each day, Earth gets hit by about 800 meteorites with a mass greater than 100 grams—enough to cause personal injury. These space rocks come in various sizes and shapes.
The chances of a meteorite hitting an individual are incredibly slim because they are spread over Earth’s vast surface. However, when they do strike, they can cause significant damage. Understanding the rare probability of encountering a meteorite impact firsthand can underscore the sheer size of Earth and how sparse these events are.
Such insights also highlight the importance of large-scale studies to comprehend cosmic events' probability, further emphasizing our tiny existence in the vast universe.

Mathematical estimation involves approximating values to make calculations more manageable, which is what we did in this exercise. We estimated the significant figures and utilized these approximations to perform the probability calculations.
We began with simplified values, such as Earth’s surface area (\[5 \times 10^{14} \] square meters), and daily meteorite impacts (800 per day). These approximations allowed us to understand and calculate the overall probability without dealing with excessively precise numbers that would complicate our computations.
By efficiently estimating each step, we turned a complex real-world problem into a more comprehendible and solvable one.