Complete Geometric probability | One, two and three-dimensional | Introduction & examples

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Complete Geometric probability | One, two and three dimension | Introduction & examples

0:00 One dimensional geometric probability
Example 1: If x is a real number chosen randomly from [-5,5] what is the probability that x^2-x-2 is less than 0

3:13 Two dimensional geometric probability
Example 2: A square S has side length 30. A standard 20-sided die is rolled and a square T is constructed inside S with side length equal to the roll. Then a dart is thrown which lands somewhere in S. Find the probability that dart lands inside the square T?

7:50 Three dimensional geometric probability
Example 3: Alex, Bob and Charlie each pick a real number between [0,1]. What is the probability that the sum of the squares of their numbers is less than 1.

A bus arrives at a station every day at a random time between 1 PM and 1:30 PM. A person arrives at this station at 1 and waits for the bus. If at 1:15 the bus has not yet arrived, what is the probability that the person will have to wait at least an additional 5 minutes?

Two numbers are chosen randomly and uniformly [-a,a] what is the probability that the absolute value of smaller number is greater than two times absolute value of the larger number? Does the answer depend on a?

Last night, Dave and Kathy both arrived at Pizza Palace at two different random times between 10:00 p.m. and midnight. They had agreed to wait exactly 15 minutes for each other to arrive before leaving. What is the probability that Dave and Kathy were together at Pizza Palace last night between 10:00 p.m. and midnight?

If 3 real numbers are chosen randomly and uniformly from [0,1]. What is the probability that the square of one of the numbers will be greater than the sum of the squares of the other two numbers?

Three points are chosen at random on a circle. What is the probability that they are on the same semi circle?

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