Geometric probabilityGeometric probability involves the distributions of length, area, and volume for geometric objects under statedconditions. The same basic concept behind probability applies, but instead of calculating total outcomes andparticular outcomes, it often involves calculating total area and particular area of a geometric figure, and theresulted probabilityity is calculated using the formulaArea of the particular regionArea of the total regionPLet's start with an example.1. A point is chosen at random inside a circle if radius 2. What is the probability that the point is within oneunit of the center of the circle?2. A point is chosen at random inside a square which has side length 4. What is the probability that the pointis within 1 inch of a side of the square?3. In each of the following figures, find the probability that a randomly chosen point lies in the shaded region. Geometric ProbabilityNan Lin1 Warmup problems1. A six-sided die is rolled, find the probability that an even number is obtained.2. If a box contains two yellow balls and one red, what is the probability of drawing a red and a yellow if twoballs are drawn?3. Three six-sided dice are rolled. What is the probability that at least one comes up with a 5 or 6?4. There is a 20% chance it will rain today. If it rains, there is a 10% chance that we will be allowed to gooutside; otherwise, there is an 80% chance we will be able to go outside. What is the probability that we willbe allowed to go outside?Geometric probabilityGeometric probability involves the distributions of length, area, and volume for geometric objects under statedconditions. The same basic concept behind probability applies, but instead of calculating total outcomes andparticular outcomes, it often ivolves calculating total area and particular area of a geometric figure, and theresulted probability is calculated using the formulaArea of the particular regionP-Area of the total regionLet's start with an example.1. A point is chosen at random inside a circle if radius 2. What is the probability that the point is within oneunit of the center of the circle?

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1. A point is chowen at random inside a circle if radius 2. What is the probability that the point is within one unit of the center of the circle? 2. A point is chosen at random inside a square which has side length 4. What is the probability that the point is within I inch of a side of the square?