The International Space Station (ISS) orbits 350 km up, but the ISS is so large

Question

The International Space Station (ISS) orbits 350 km up, but the ISS is so large that it can be seen from Earth with the naked eye, if you know when and where to look. For this problem, assume that on a clear night, a properly trained observer has a 93% chance of seeing the ISS when it passes overhead. Eight (properly trained) students position themselves at eight different locations, each independently attempting to see the ISS.

The weather channel predicts that there is a 30% chance of raining or being cloudy when ISS will be passing tonight. If it is raining or cloudy, the probability of seeing the ISS is zero. What is the probability that all eight students will see the ISS tonight? What is the probability that at least one student will see the ISS tonight?

Explanation / Answer

0.99978

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