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

ID: 3219754 • Letter: 1

Question

1.) 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 6 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_______

2.)Continuing from the last question,

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

3.)Continuing, ...

Of the 6 probes, how many would be "expected" to land on land? Give your answer to two decimal places.____

Explanation / Answer

Solution:-

1) The chances that at least one of them will "land" on land is 0.8719.

The probability it will arrive on land = 29/100 = 0.29

Number of launched probes = 6

By applying binomial distribution:-

P(x, n, p) = nCx*p x *(1 - p)(n - x)

P(x > 1) = 0.8719

2) The chances that exactly two of the probes will "land" on land is 0.3206.

The probability it will arrive on land = 29/100 = 0.29

Number of launched probes = 6

By applying binomial distribution:-

P(x, n, p) = nCx*p x *(1 - p)(n - x)

P(x = 2) = 0.3206

3) The expected number of probes that will "land" on land is 1.74.

E(x) = n × p

E(x) = 6 × 0.29

E(x) = 1.74