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

Question

The International Space Station (ISS) orbits 350 km up, but the ISS is so big that it can be seen from Earth with the naked eye (if you are trained to know when and where to look, and the sky is clear). For this problem, assume that on a clear night, a properly trained observer has a 90% chance of seeing the ISS when it passes overhead. Assume that the ISS will be passing overhead tonight in New York and the sky will be clear. Ten (properly trained) members of the New York Astronomy Club position themselves at ten different locations in New York, each independently attempting to see the ISS. What is the probability that all ten members of the club will see the ISS tonight? What is the probability that none of the members of the club will see the ISS tonight? For this part of the problem, keep 5 decimal places accuracy in your answer.

Explanation / Answer

let X denotes the number of properly trained members who will see the ISS out of the 10 members

each of the members are looking independently

and there is 90% chance of a trained member to see the ISS with naked eye

so X~Bin(10,0.90)

pmf of X is P[X=x]=10Cx0.90x0.1010-x   x=0,1,2,3,...,10

a) so the probability that all ten members of the club will see the ISS tonight is

P[X=10]=10C100.9010=0.348678 [answer]

b) the probability that none of the members of the club will see the ISS tonight is

P[X=0]=10C00.110=0.00000 [answer]

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.