Only 29% of the surface of the Earth is land; the rest is covered by water. Alie

Question

Only 29% of the surface of the Earth is land; the rest is covered by water. Aliens from the planet Tralfamador have launched a set of 15 probes to land at completely random locations throughout the Earth. They are searching for intelligent life.

For each probe, the probability it will arrive on land is therefore 29%. What are the chances that at least one of them will "land" on land? Use at least four decimal places.

Continuing from the last question,

What are the chances that exactly two of the probes will "land" on land?

Continuing, ...

Of the 15 probes, how many would be "expected" to land on land? Give your answer to two decimal places.

Explanation / Answer

Probability that a probe will launch on land is 0.29

This problem is of binomial distribution.
Probability that exactly two of the probes will "land" on land
P(X=2) = 15C2 * (0.29)^2 * (1-0.29)^13
P(X=2) = 0.1029

Hence probability that exactly two probe will land on land.

Expected number of probes that would be land on land = 15 * 0.29 = 4.35

Related Questions

Navigate

• Browse (All)
• Browse O
• Subjects

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