Discrete Mathematics

Geometric Probability

1-dimensional Geometric Probability

         

A real number r r is chosen at random from the interval [1,1] [ -1 , 1 ] .

What is the probability that r2<19 r ^ 2< \frac{1}{9} ?

A real number is chosen at random from the interval [5,12] [ -5, 12 ] . What is the probability that the real number is less than 1 1 ?

A point is chosen uniformly at random on the real line, in the interval (0,1) (0, 1) . What is the probability that the chosen point is closer to the point 00 than it is to the point 0.38 0.38 ?

Two integers are randomly and independently chosen from 1313 to 2222 (inclusive). Now, Kevin picks an integer from 1313 to 2222 wanting the probability that his number is not less than either of two to be more than 5050%. What is the least number he can pick?

Details and assumptions

The two numbers randomly and independently chosen could be the same.

A point is chosen at random from the unit interval [0,1] [0, 1] . What is the probability that it is closer to 0.66 0.66 than it is to 0.28 0.28 ?

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