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# Geometric Probability

Sometimes, probability questions can be interpreted geometrically, from simple examples like throwing darts to surprising applications like catching the bus!

# 1-dimensional Geometric Probability

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

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

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

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

Two integers are randomly and independently chosen from $$13$$ to $$22$$ (inclusive). Now, Kevin picks an integer from $$13$$ to $$22$$ wanting the probability that his number is not less than either of two to be more than $$50$$%. 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 $$[0, 1]$$. What is the probability that it is closer to $$0.66$$ than it is to $$0.28$$?

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