The International Space Station ISS orbits 350 km up but the

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. Assume that the ISS will be passing overhead tonight and skies will be clear. Eight (properly trained) members of the Astronomy Club position themselves at eight different locations, each independently attempting to see the ISS.

Part A: What is the probability that all eight members of the club will see the ISS tonight?

Solution

Probability will be determined by multiplying the individual probabilities of each observer:

P = 0.93*0.93*0.93*0.93...

Or just

P = 0.93 ^ 8 = 0.5596 or 55.96% probability