(A) What Fraction of the Random Numbers Are Smaller Than

question 54

Essay

(A) What fraction of the random numbers are smaller than 0.5?
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(B) What fraction of the time is a random number less than 0.5 followed by another random number less than 0.5?
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(C) What fraction of the random numbers are larger than 0.8?
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(D) What do you expect the answers to (A), (B) and (C) to be before simulating? Do the answers you provided to those questions match your expectations? Explain why or why not.
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(E) Suppose your answers to (A), (B) and (C) are not close to the expected answers. What can you do to obtain answers from the simulation that are closer to the expected answers?

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Definitions:

Lunar Highlands

Rough, mountainous regions on the moon's surface, characterized by their lighter color and higher altitude than the lunar maria.

Mare

Latin for "sea," often used to describe the large, dark basaltic plains on the Moon, formed by ancient volcanic eruptions.

Lunar Highlands

Elevated, mountainous regions on the moon's surface, characterized by high albedo, heavy cratering, and made predominantly of anorthosite.

Impact Craters

Circular depressions formed by the collision of a meteorite, asteroid, or comet with the Earth's surface, characterized by a raised rim and, in some cases, a central peak.