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 \( 0.28 \)?