Geometric Probability

2-dimensional Geometric Probability


If we randomly choose two numbers aa and bb from the interval [0,1],[0,1], what is the probability that the quadratic x2+ax+b=0x^2+ax+b=0 has two distinct real roots?

What is the probability that x2+ax+b=0x^2+ax+b=0 has no real roots when aa and bb are two randomly chosen numbers from the interval [0,2]?[0,2]?

Rachel and Ross will go to the gas station at a random time between 4 and 5 o'clock. If it takes exactly ten minutes for each person to refill his/her car and get out of the gas station, what is the probability that they meet at the gas station?

In the figure above, ABCD\square ABCD is a square with side length 1. Find the probability that PAB\triangle PAB is an obtuse triangle, when PP is a randomly chosen point inside ABCD.\square ABCD.

The figure above shows the base (of radius 11 cm) of a cylindrical bucket. There is a red circle of radius 4 cm centered at the center of the base. If Tom throws a coin of radius 1 cm into this bucket, what is the probability that the coin will land in contact with the perimeter of the red circle?


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